No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Design of intelligent computing solver with Morlet wavelet neural networks for nonlinear predator–prey model
Abstract
The design of integrated intelligent computing solver with Morlet wavelet neural networks (MW-NNs) is presented for solving the mathematical predator–prey model by exploiting the strength of MW-NNs modeling, optimization ability of global search with genetic algorithms (GAs) and rapid local search eminence of sequential quadratic programming (SQP), i.e., MW-NNs-GA-SQP. The proposed MW-NNs-GA-SQP scheme is used to analyze the predator–prey dynamics for six different variables coefficient values. The validation, correctness and reliability of the presented MW-NNs-GA-SQP technique is attained through the consistent matched outcomes with the reference Adams numerical results. Moreover, statistics investigations have been accomplished to verify the precision and accuracy of the outcomes with proposed MW-NNs-GA-SQP solver via the performances of Theil’s inequality coefficient, Nash Sutcliffe efficiency and mean absolute error.
... The nonlinear Lienard differential Model is also solved by the ANN-based solver [8]. ANN-based numerical solvers are also widely used to solve the nonlinear physical problem for instance, predator pre-model [9], lane Emden Model [10,11], film flow model [12], mass and heat transfer model [13], short-term hydrothermal coordination [14], large scale system [15], Emden-Fowler problem [16], life Cycle Optimization problem [17], Flierl equations [18,19], heat condition model [13,20], Singular Periodic boundary problem [21], prey-Predictive system [9,22], Smoke Problem [23], nervous stomach model [24], Engineering problems [25], Transport system [26], the Love story of Layle [27], and the monkeypox systems [28,29]. ...
... The nonlinear Lienard differential Model is also solved by the ANN-based solver [8]. ANN-based numerical solvers are also widely used to solve the nonlinear physical problem for instance, predator pre-model [9], lane Emden Model [10,11], film flow model [12], mass and heat transfer model [13], short-term hydrothermal coordination [14], large scale system [15], Emden-Fowler problem [16], life Cycle Optimization problem [17], Flierl equations [18,19], heat condition model [13,20], Singular Periodic boundary problem [21], prey-Predictive system [9,22], Smoke Problem [23], nervous stomach model [24], Engineering problems [25], Transport system [26], the Love story of Layle [27], and the monkeypox systems [28,29]. ...
The current study aims to present a swarm-optimized technique for the numerical treatment of dengue fever non-linear model. The model is composed of the coupled nonlinear system comprising the susceptible, infected, and recovered compartments. The system is transformed into an unsupervised single layer feed-forward artificial neural network with a Mexican hat wavelet activation function in the hidden layer. The unknowns of the neural network is optimized with particle swarm optimization as an efficient global search aided by the effective local search technique based on sequential quadratic programming. The presented results are compared with state of art Runge-Kutta method and other modern reported techniques on various performance indicators like absolute error, mean average deviation, global absolute error, global mean average deviation, convergence, and computational complexity. Comprehensive Monte Carlo simulations and their statistical analysis are presented to ensure accuracy, consistency in convergence, and computational complexity in terms of execution time. It is observed that the proposed scheme is accurate, reliable, convergent, and computationally viable in treating the nonlinear coupled system under consideration.
... Heuristic algorithms are effective methods for solving parameter calibration problems. Heuristic search algorithms do not require information such as continuous and differentiable objective functions and have good global optimization capabilities, making them a hot topic in the field of optimization [48][49][50]. ...
The reliability of urban transportation systems is crucial for ensuring smooth traffic flow and minimizing disruptions caused by external factors. This study focuses on improving the stability and efficiency of transportation systems through the calibration of a refined link performance function while building upon the U.S. Bureau of Public Roads (BPR) model. To achieve this, we propose three customized algorithms—Newton’s method, Bayesian optimization, and the differential evolutionary algorithm—to calibrate the key parameters. Additionally, we conducted a sensitivity analysis to assess the influences of the model parameters on link performance. Numerical experiments conducted in Yuyao City demonstrate the applicability and efficacy of the proposed model and solution algorithms. Our results reveal that the Newton approach is notably more efficient than the Bayesian optimization algorithm and the differential evolutionary algorithm.
... In this context, we draw upon a body of prior research to contextualize our study and highlight the relevance of our work in the face of contemporary challenges such as global warming. The key works presented in [52][53][54][55][56] have contributed to the understanding and analysis of predator-prey systems, providing valuable insights into the dynamics and behavior of these ecological interactions. These studies represent a comprehensive body of work that explores various computational and mathematical techniques for understanding predator-prey dynamics. ...
This research paper presents an eco-epidemiological model that investigates the intricate dynamics of a predator–prey system, considering the impact of fear-induced stress, hunting cooperation, global warming, and memory effects on species interactions. The model employs fractional-order derivatives to account for temporal dependencies and memory in ecological processes. By incorporating these factors, we aim to provide a more comprehensive understanding of the underlying mechanisms that govern the stability and behavior of ecological systems. Mathematically we investigate system’s existence, equilibria and their stability. Moreover, global stability and hopf bifurcation also analyzed in this study. Numerical simulations have been performed to validate the analytical results. We find that the coexistence equilibrium is stable under specific conditions, along with the predator equilibrium and the disease-free equilibrium. Bifurcation analyses demonstrate the intricate behavior of species densities in response to changes in model parameters. Fear and global warming are found to stabilize the system, while cooperation and additional food for predators lead to destabilization. Additionally, the influence of species memory has been explored. We observe that memory tends to stabilize the system as species memory levels increase.
... We can also consider impulsive delayed harvesting or stage structure of prey/predator populations, which will lead to richer dynamics [30]. In addition, trying to solve system (6) using an intelligent computational solver, or different numerical methods such as the Galerkin method or Legendre wavelet algorithm will also be interesting work [31][32][33]. ...
Harvesting is one of the ways for humans to realize economic interests, while unrestricted harvesting will lead to the extinction of populations. This paper proposes a predator–prey model with impulsive diffusion and transient/nontransient impulsive harvesting. In this model, we consider both impulsive harvesting and impulsive diffusion; additionally, predator and prey are harvested simultaneously. First, we obtain the subsystems of the system in prey extinction and predator extinction. We obtain the fixed points of the subsystems by the stroboscopic map theories of impulsive differential equations and analyze their stabilities. Further, we establish the globally asymptotically stable conditions for the prey/predator-extinction periodic solution and the trivial solution of the system, and then the sufficient conditions for the permanence of the system are given. We also perform several numerical simulations to substantiate our results. It is shown that the transient and nontransient impulsive harvesting have strong impacts on the persistence of the predator–prey model.
The present study performs the design of a novel Gudermannian neural networks (GNNs) for the nonlinear dynamics of prey-predator system (NDPPS). The process of GNNs is applied using the global and local search approaches named as genetic algorithm and interior-point algorithms, i.e., GNNs-GA-IPA. An error-based merit function is constructed using the NDPPS and its initial conditions and then optimized by the hybrid of GA-IPA. Six cases of the NDPPS using the variable coefficients have been presented and the correctness is observed through the overlapping of the obtained and Runge-Kutta reference results. The results of the NDPPS have been performed between 0 and 5 using the step size 0.02. The graph of absolute error are performed around 10⁻⁰⁶ to 10⁻⁰⁸ to check the consistency of the proposed GNNs-GA-IPA. The statistical analysis based minimum, median and semi-interquartile ranges have been performed for both predator and prey dynamics of the model. Moreover, the investigations through the statistical operators are performed to validate the reliability of the obtained outcomes based on multiple trials.
The present study presents numerical solution of the fourth order, singular, nonlinear Emden-Fowler equation integrated computational intelligence by exploiting the efficiency of feedforward artificial neural networks (ANNs), global optimization strength of genetic algorithms (GAs) and rapid local search of sequential quadratic programming (SQP). ANN is applied to discretize the nonlinear Emden-Fowler differential equation and consequentially construct a fitness/merit function on mean squared error sense. The optimization of the decision variables of ANN to solve the multi-singular, fourth order, nonlinear Emden-Fowler equation is performed by integrating capability GAs and SQP. The proficiency of the presented approach is certified on precision, convergence and stability indices, which are further enhanced through effectiveness, significance and reliability measures on statistical data for solving three different cases of the singular systems.
In this paper, a novel meta-heuristic computing solver is presented for solving the singular three-point second-order boundary value problems using artificial neural networks (ANNs) optimized by the combined strength of global and local search ability of genetic algorithms (GAs) and interior point algorithm (IPA), i.e., ANN–GA–IPA. The inspiration for presenting this numerical work comes from the intention of introducing a consistent framework that combines the effective features of neural networks optimized with the contexts of soft computing to handle with such challenging systems. Three numerical variants of singular second-order system have been taken to examine the proficiency, robustness, and stability of the designed approach. The comparison of the proposed results of ANN–GA–IPA from available exact solutions shows the good agreement with 5 to 7 decimal places of the accuracy which established worth of the methodology through performance analyses on a single and multiple executions.
In this study, a novel neuro-swarming computing solver is developed for numerical treatment of third-order nonlinear multi-singular Emden–Fowler equation (TONMS-EFE) by using function approximation ability of artificial neural networks (ANNs) modeling and global optimization mechanism of particle swarm optimization (PSO) integrated with local search of interior-point scheme (IPS), i.e., ANN-PSO-IPS. The inspiration for the design of ANN-PSO-IPS-based numerical solver comes with an objective of presenting a reliable, accurate and viable structure that combines the strength of ANNs optimized with the integrated soft computing frameworks to deal with such challenging systems based on TONMS-EFE. The proposed ANN-PSO-IPS is implemented for four variants of TONMS-EFEs, and comparison with exact solutions relieved its robustness, correctness and effectiveness, which is further authenticated through statistical explorations.
In this paper, we have extended the Fractional Differential Transform method for the numerical solution of the system of fractional partial differential-algebraic equations. The system of partial differential-algebraic equations of fractional order is solved by the Fractional Differential Transform method. The results exhibit that the proposed method is very effective.
Infectious diseases have caused the death of many people throughout the world for centuries. For this purpose, many researchers have investigated these diseases for establishing new treatment and protective measures. The most important of these is HIV disease. In this study, an HIV infection model of CD 4 ⁺T cells is handled comprehensively with the newly defined Atangana-Baleanu (AB) fractional derivative. The existence and uniqueness of the solutions for fractionalized HIV disease model with the new derivative by considering the Arzela-Ascoli theorem.
In this paper, our aim is to generalize the truncated M-fractional derivative which was recently introduced [Sousa and de Oliveira, A new truncated M-fractional derivative type unifying some fractional derivative types with classical properties, Inter. of Jour. Analy. and Appl., 16 (1), 83–96, 2018]. To do that, we used generalized M-series, which has a more general form than Mittag-Leffler and hypergeometric functions. We called this generalization as truncated ℳ-series fractional derivative. This new derivative generalizes several fractional derivatives and satisfies important properties of the integer-order derivatives. Finally, we obtain the analytical solutions of some ℳ-series fractional differential equations.
Forecasting of fast fluctuated and high-frequency financial data is always a challenging problem in the field of economics and modelling. In this study, a novel hybrid model with the strength of fractional order derivative is presented with their dynamical features of deep learning, long-short term memory (LSTM) networks, to predict the abrupt stochastic variation of the financial market. Stock market prices are dynamic, highly sensitive, nonlinear and chaotic. There are different techniques for forecast prices in the time-variant domain and due to variability and uncertain behavior in stock prices, traditional methods, such as data mining, statistical approaches, and non-deep neural networks models are not suited for prediction and generalized forecasting stock prices. While autoregressive fractional integrated moving average (ARFIMA) model provides a flexible tool for classes of long-memory models. The advancement of machine learning-based deep non-linear modelling confirms that the hybrid model efficiently extracts profound features and model non-linear functions. LSTM networks are a special kind of recurrent neural network (RNN) that map sequences of input observations to output observations with capabilities of long-term dependencies. A novel ARFIMA-LSTM hybrid recurrent network is presented in which ARFIMA model-based filters having the linear tendencies better than ARIMA model in the data and passes the residual to the LSTM model that captures nonlinearity in the residual values with the help of exogenous dependent variables. The model not only minimizes the volatility problem but also overcome the over fitting problem of neural networks. The model is evaluated using PSX company data of the stock market based on RMSE, MSE and MAPE along with a comparison of ARIMA, LSTM model and generalized regression radial basis neural network (GRNN) ensemble method independently. The forecasting performance indicates the effectiveness of the proposed AFRIMA-LSTM hybrid model to improve around 80% accuracy on RMSE as compared to traditional forecasting counterparts.
This paper deals with an approach to obtaining the numerical solution of the Lotka–Volterra predator-prey models with discrete delay using Euler polynomials connected with Bernoulli ones. By using the Euler polynomials connected with Bernoulli ones and collocation points, this method transforms the predator-prey model into a matrix equation. The main characteristic of this approach is that it reduces the predator-prey model to a system of algebraic equations, which greatly simplifies the problem. For these models, the explicit formula determining the stability and the direction is given. Numerical examples illustrate the reliability and efficiency of the proposed scheme.
In this study, a novel computational paradigm based on Morlet wavelet neural network (MWNN) optimized with integrated strength of genetic algorithm (GAs) and Interior-point algorithm (IPA) is presented for solving second order Lane–Emden equation (LEE). The solution of the LEE is performed by using modelling of the system with MWNNs aided with a hybrid combination of global search of GAs and an efficient local search of IPA. Three variants of the LEE have been numerically evaluated and their comparison with exact solutions demonstrates the correctness of the presented methodology. The statistical analyses are performed to establish the accuracy and convergence via the Theil’s inequality coefficient, mean absolute deviation, and Nash Sutcliffe efficiency based metrics.
In the current paper, we carry out an investigation into the exact solutions of the (3+1)-dimensional space-time fractional modified KdV–Zakharov–Kuznetsov (fractional mKdV–ZK) equation. Based on the conformable fractional derivative and its properties, the fractional mKdV–ZK equation is reduced into an ordinary differential equation which has been solved analytically by the variable separated ODE method. Various types of analytic solutions in terms of hyperbolic functions, trigonometric functions and Jacobi elliptic functions are derived. All conditions for the validity of all obtained solutions are given.
Here, the authors analyse the fractional-order predator-prey model with uncertainty, due to the vast applications in various ecological systems. The most of the ecological model do not have exact analytic solution, so they proposed a numerical technique for an approximate solution. In the proposed method, they have implemented the higher order term into the fractional Euler method to enhance the precise solution. Further, the present attempt is aimed to discuss the solutions of the FPPM with uncertainty (fuzzy) initial conditions. The initial conditions of the predator-prey model were taken as fuzzy initial conditions due to the fact that the ecological model highly depends on uncertain parameters such as growth/decay rate, climatic conditions, and chemical reactions. Finally, the numerical example manifest that the proposed method is authentic, applicable, easy to use from a computational viewpoint and the acquired outcomes are balanced with the existing method (HPM), which shows the efficiency of the proposed method.
In this study, numerical solutions of the fractional Harry Dym equation are investigated. Linearization techniques are utilized for non-linear terms existing in the fractional Harry Dym equation. The error norms L2 and L∞ are computed. Stability of the finite difference method is studied with the aid of Von Neumann stabity analysis.
Bio-inspired computing approaches are effective to solve a variety of dynamical problems. The strength of these stochastic solvers is exploited for the numerical treatment of a nonlinear heat conduction model of the human head using artificial neural networks (ANNs), genetic algorithms (GAs), active-set technique (AST), and their hybrids. The universal function approximation competencies of unsupervised ANNs are utilized in constructing the mathematical model of the problem by defining an error function in the mean squared sense. The training of the design parameters of ANN models is made with global search brilliance of GAs, viably local search with AST and hybrid approach GA-AST. The results of the proposed schemes are determined in terms of temperature profiles by considering variants of the problem with different Biot numbers, metabolic thermogenesis slope parameters and thermogenesis heat production factors. The correctness, effectiveness and convergence of the proposed approaches are also ascertained through statistics. © 2018, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.
Many ecological systems show striking non-homogeneous population distributions. Diffusion-driven instabilities are commonly studied as mechanisms of pattern formation in many fields of biology but only rarely in ecology, in part because some of the conditions seem quite restrictive for ecological systems. Seasonal variation is ubiquitous in temperate ecosystems, yet its effect on pattern formation has not yet been explored. We formulate and analyze an impulsive reaction–diffusion system for a resource and its consumer in a two-season environment. While the resource grows throughout the ‘summer’ season, the consumer reproduces only once per year. We derive conditions for diffusion-driven instability in the system, and we show that pattern formation is possible with a Beddington–DeAngelis functional response. More importantly, we find that a low overwinter survival probability for the resource enhances the propensity for pattern formation: diffusion-driven instability occurs even when the diffusion rates of prey and predator are comparable (although not when they are equal).
Designing optimization models and meta-heuristic algorithms for minimization of traveling routes of vehicles in solid waste collection has been gaining interest in environmental modeling. The computer models and methods are useful to bring out specific strategies for prevention and precaution of possible disasters that could be foreseen worldwide. This paper proposes a new Spatial Geographic Information System (GIS)-based Genetic Algorithm for optimizing the route of solid waste collection. The proposed algorithm, called SGA, uses a modified version of the original Dijkstra algorithm in GIS to generate optimal solutions for vehicles. Then, a pool of solutions, which are optimal routes of all vehicles, is encoded in Genetic Algorithm. It is iteratively evolved to a better one and finally to the optimal solution. Experiments on the case study at Sfax city in Tunisia are performed to validate the performance of the proposal. It has been shown that the proposed method has better performance than the practical route and the original Dijkstra method.
The aim of the present work is to investigate the stochastic numerical solutions of nonlinear Painlevé II systems arising from studies of two-dimensional Yang-Mills theory, growth processes through fluctuation formulas in statistical physics, soft-edge random matrix distributions using the strength of bio-inspired heuristics through artificial neural networks (ANNs), genetic algorithm (GA)-based evolutionary computations and interior-point techniques (IPTs). A new mathematical modelling of the system is formulated through ANNs by defining an error function that exactly satisfies the initial conditions. The weights of ANN models optimized through a memetic computing approach that is based on a global search with GAs, and IPTs are used for an efficient local search. The designed scheme is substantiated through comparative analysis with a fully explicit Range-Kutta numerical procedure on nonlinear Painlevé II systems by taking different magnitudes of forcing factors. The accuracy and convergence of the proposed scheme are validated through statistics performed on large numbers of simulations. © 2018, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.
In this paper, we modeled a four-level integrated supply chain, contains a supplier, a producer, a wholesaler and multiple retailers. These four levels interacted and agreed with each other on having the same period length and same number of stockpile for each product in order to make an integrated chain to minimize total cost of supply chain. Products in this model are multi stage and there is limitation on production time capacity for producing the products. Other constraints of this model include: limitation on "total procurement cost, production cost, number of orders, space cost, number of stockpile for each level and setup cost". Objectives are to find both the number of agreed optimum stockpile and the agreed optimum period length for products that levels agree to minimize total inventory cost of chain while the constraints are satisfied. Problem model is nonlinear and large, so sequential quadratic programming (SQP) as one of the best exact optimization methods for solving nonlinear and large problems is used to solve this model. Three numerical examples are solved in order to demonstrate the applicability of this model and to evaluate SQP optimum performance. The results illustrate that SQP method has high efficiency in terms of optimum solutions, number of iterations to achieve the optimum solution, infeasibility, optimality error and complementarity for solving research nonlinear and large model. At the end, a sensitivity analysis is performed on the change rate of the obtained integrated objective function based on the change rate of the number of stockpile.
In this paper, a bio-inspired computational intelligence technique is presented for solving nonlinear doubly singular system using artificial neural networks (ANNs), genetic algorithms (GAs), sequential quadratic programming (SQP) and their hybrid GA–SQP. The power of ANN models is utilized to develop a fitness function for a doubly singular nonlinear system based on approximation theory in the mean square sense. Global search for the parameters of networks is performed with the competency of GAs and later on fine-tuning is conducted through efficient local search by SQP algorithm. The design methodology is evaluated on number of variants for two point doubly singular systems. Comparative studies with standard results validate the correctness of proposed schemes. The consistent correctness of the proposed technique is proven through statistics using different performance indices.
In this study, strength of evolutionary computational intelligence based on genetic algorithms (GAs) is exploited for parameter identification of nonlinear Hammerstein controlled autoregressive (NHCAR) systems. The fitness function is constructed for the NHCAR system by defining an error function in the mean square sense. Unknown adjustable weights of the system are optimized with GAs, used as an effective tool for effective global search. Comparative analysis of the proposed scheme is made from true parameters of the systems for a number of scenarios based on different levels of signal-to-noise ratios. The validation of the performance is made through statistics based on sufficiently large number of runs using indices of mean absolute error, variance account for, and Thiel’s inequality coefficient as well as their global versions.
This paper reflects some research outcome denoting as to how Lotka–Volterra prey predator model has been solved by using the Runge–Kutta–Fehlberg method (RKF). A comparison between Runge–Kutta–Fehlberg method (RKF) and the Laplace Adomian Decomposition method (LADM) is carried out and exact solution is found out to verify the applicability, efficiency and accuracy of the method. The obtained approximate solution shows that the Runge–Kutta–Fehlberg method (RKF) is a more powerful numerical technique for solving a system of nonlinear differential equations.
In this study, a novel design of integrated biological inspired computational heuristics is presented for the dynamics of nonlinear unipolar electrohydrodynamic (UP-EHD) pump flow model by exploiting the competency of finite difference method (FDM) for discretization, global search viability of genetic algorithms (GAs) and local search efficiency of active-set method (ASM), i.e., FDM-GA-ASM. The FDM is incorporated to transform the differential equations of the UP-EHD pump flow model into a system of nonlinear algebraic equations. The cost function is constructed through the mean-square residual error by mimicking forward, central and backward difference schemes viable for a broader range of physical models. The optimum solution is achieved by the integration of global search with GAs and local search of ASM for speedy refinements. The designed stochastic numerical solver FDM-GA-ASM investigates the critical physical parameters, i.e., charge density, electric field and electric potential by varying electrical slip, Reynolds number and source number of the UP-EHD model. Statistical observations in terms of probability plots, histogram illustrations, boxplots for the cost function, mean absolute error, root mean squared error and Nash-Sutcliffe efficiency metrics are used to validate the efficiency of the FDM-GA-ASM scheme for the three variants of the UP-EHD model. The designed FDM-GA-ASM is a promising numerical computing solver for nonlinear differential systems in engineering and technology.
In this paper, the design of stochastic computational intelligent solver is presented for the solution of mathematical model representing the dynamics of mosquito dispersal in a heterogeneous environment by feedforward artificial neural networks (FFANNs) trained with genetic algorithms (GAs) aided with sequential quadratic programming (SQP), i.e., FFANN-GASQP. In the scheme FFANN-GASQP, the formulation of fitness function in mean square error sense with continuous mapping-based differential equation models of FFANNs for the mosquito dispersal system and training of these networks are accomplished by integrated competency of GA and SQP. The exactness, reliability and stability of the designed FFANN-GASQP approach are established through comparative studies with Adams numerical results for both single and multiple runs. Outcomes of statistical assessments are used to validate the accuracy and convergence of the designed FFANN-GASQP scheme.
The aim of the present study is to solve the singular second-order functional differential model with the development of neuro-swarm intelligent computing solver ANN–PSO–SQP based on mathematical modeling of artificial neural networks (ANNs) optimized globally search efficacy of particle swarm optimization (PSO) aided with local search efficiency of sequential quadratic programming (SQP). In the scheme ANN–PSO–SQP, an error-based objective function is assembled with the help of continuous mapping of ANN for second-order singular functional differential model and optimized with combination strength of PSO with SQP. The inspiration for the design of ANN–PSO–SQP comes with an objective to present a precise, reliable and feasible frameworks to handle with stiff singular functional models involving the delayed, pantograph and prediction terms. The designed scheme is tested for three different variants of the singular second-order functional differential models. The obtained outcomes on both single as well as multiple runs of the proposed ANN–PSO–SQP are compared with the exact solutions to validate the efficacy, correctness and viability.
The intension of the present work is to present the stochastic numerical approach for solving human immunodeficiency virus (HIV) infection model of cluster of differentiation 4 of T-cells, i.e., CD4+ T cells. A reliable integrated intelligent computing framework using layered structure of neural network with different neurons and their optimization with efficacy of global search by genetic algorithms supported with rapid local search methodology of active-set method, i.e., hybrid of GA-ASM, is used for solving the HIV infection model of CD4+ T cells. A comparison between the present results for different neurons-based models and the numerical values of the Runge–Kutta method reveals that the present intelligent computing techniques is trustworthy, convergent and robust. Statistics-based observation on different performance indices further demonstrates the applicability, effectiveness and convergence of the present schemes.
In this study, an efficient soft computing paradigm is presented for solving Bagley-Torvik systems of fractional order arising in fluid dynamic model for the motion of a rigid plate immersed in a Newtonian fluid using feed-forward fractional artificial neural networks (FrANNs) and sequential quadratic programming (SQP) algorithm. The strength of FrANNs has been utilized to construct an accurate modeling of the equation using approximation theory in mean square error sense. Training of weights of FrANNs are performed with SQP techniques. The designed scheme has been examined on different variants of the systems. The comparative studies of the proposed solutions with available exact, as well as, reference numerical results demonstrate the worth and effectiveness of the solver. The accuracy, consistency, and complexity is evaluated in-depth through results of statistics.
The ratio-dependent predator–prey model exhibits rich dynamics due to the singularity of the origin. Harvesting in a ratio-dependent predator–prey model is relatively an important research project from both ecological and mathematical points of view. In this paper, we study the temporal, spatial and spatiotemporal dynamics of a ratio-dependent predator–prey diffusive model where the predator population harvest at catch-per-unit-effort hypothesis. For the spatially homogeneous model, we derive conditions for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solution by the center manifold and the normal form theory. For the reaction–diffusion model, firstly it is shown that Turing (diffusion-driven) instability occurs, which induces spatial inhomogeneous patterns. Then it is demonstrated that the model exhibit Hopf bifurcation which produces temporal inhomogeneous patterns. Finally, the existence and non-existence of positive non-constant steady-state solutions are established. Moreover, numerical simulations are performed to visualize the complex dynamic behavior.
A new computational intelligence numerical scheme is presented for the solution of second order nonlinear singular functional differential equations (FDEs) using artificial neural networks (ANNs), global operator genetic algorithms (GAs), efficient local operator interior-point algorithm (IPA), and the hybrid combination of GA-IPA. An unsupervised error function is assembled for the DDE optimized by ANNs using the hybrid combination of GA-IPA. Three kinds of the second order nonlinear singular DDEs have been solved numerically and compared their results with the exact solutions to authenticate the performance and exactness of the present designed scheme. Moreover, statistical analysis based on Mean absolute deviation, Theil's inequality coefficient and Nash Sutcliffe efficiency is also performed to validate the convergence and accuracy of the present scheme.
The electrical muscle stimulation models (EMSMs) are effectively described through Hammerstein structure and are used to restore the functionality of paralyzed muscles after spinal cord injury (SCI). In the present study, global search efficacy of evolutionary computing paradigm through backtracking search algorithm (BSA) is exploited for parameter estimation of EMSMs. The approximation theory in mean squared error sense is used for the construction of a merit function for EMSMs based on deviation between optimal and approximated parameters. Variants of BSA are designed based on memory size and population dynamics for the minimization problem of EMSMs having cubic spline as well as sigmoidal nonlinearities. Comparative studies by means of rigorous statistics establish the worth of scheme for effective, accurate, reliable, robust and stable identification of EMSMs in rehabilitation scenarios of SCI.
One of the major applications of the nonlinear system of differential equations in biomathematics is to describe the predator–prey problem. In this framework, the fractional predator–prey model with Beddington-DeAngelis is examined. This model is formed of three nonlinear ordinary differential equations to describe the interplay among populations of three species including prey, immature predator, and mature predator. The fractional operator used in this model is the Atangana–Baleanu fractional derivative in Caputo sense. We show first that the fractional predator–prey model has a unique solution, then propose an efficient numerical scheme based on the product integration rule. The numerical simulations indicate that the obtained approximate solutions are in excellent agreement with the expected theoretical results. The numerical method used in this paper can be utilized to solve other similar models.
In the present study, strength of meta-heuristic computing techniques is exploited for estimation problem of Hammerstein controlled auto regressive auto regressive moving average (HCARARMA) system using differential evolution (DE), genetic algorithms (GAs), pattern search (PS) and simulated annealing (SA) algorithms. The approximation theory in mean squared error sense is utilized for construction of cost function for HCARARMA model and highly uncorrelated adjustable parameter of the system is optimized with global search exploration of DE, GAs, PS and SA algorithms. Comparative study is carried out from desired known parameters of the HCARARMA model for different degree of freedom and noise variation scenarios. Performance analysis of the DE, GAs, PS and SA algorithms is conducted through results of statistics based on sufficient large independent executions in terms of measure of central tendency and variation for both precision and complexity indices. The exhaustive simulations established that the population-based heuristics are more accurate than single solution-based methodologies for HCARARMA identification.
We consider the model of interaction of predator and prey with omnivore using three different waiting time distributions. The first waiting time is induced by the power law distribution which is the generator of Pareto statistics. The second waiting time is induced by exponential decay law with a particular property of Delta Dirac distribution when the fractional order tends to 1, this distribution is link to the Poison distribution. While the last waiting distribution, induced by the Mittag-Leffler distribution, presents a crossover from exponential to power law. For each model, we presented the conditions under which the existence of unique set of exact solutions is reached using the fixed-point Picard’s method. Making use of a recent suggested numerical scheme, we solved each model numerically and some numerical simulations were generated for different values of fractional orders. We noticed a new attractor which can be considered as a combination of the Brownian motion and power law distribution in the model with the Atangana-Baleanu fractional derivative. With the aim to capture more attractors, we modified the model and presented also some numerical simulations. Our new model provides more attractors than the existing one even for fractional differential cases. We presented finally the Maximal Lyapunov exponent and the bifurcation diagrams. The comparative study shows that modeling with non-local and non-singular kernel fractional derivative leads to more attractors as this kernel is able to capture more physical problems.
This article is being retracted effective 7 July 2020.
In this paper, we address the optimal power flow problem in dc grids (OPF-DC). Our approach is based on sequential quadratic programming which solves the problem associated with non-convexity of the model. We propose two different linearizations and compare them to a non-linear algorithm. The first model is a Newton-based linearization which takes the Jacobian of the power flow as a linearization for the optimization stage, and the second model uses the nodal currents as auxiliary variables to linearize over the inequality constraints. Simulation results in radial and meshed grids demonstrate the efficiency of the proposed methodology and allow finding the same solution given by the exact nonlinear representation of the OPF-DC problem.
The eigenvalues and eigenvectors of a matrix have many applications in engineering and science, such us studying and solving structural problems in both the treatment of signal or image processing, and the study of quantum mechanics. One of the most important aspects of an algorithm is the speed of execution, especially when it is used in large arrays. For this reason, in this paper the authors propose a new methodology using a genetic algorithm to compute all the eigenvectors and eigenvalues in real symmetric and Hermitian matrices. The algorithm uses a general-purpose library developed by the authors for genetic algorithms (GALGA). The speed of execution and the influence of population size have been studied. Moreover, the algorithm has been tested in different matrices and population sizes by comparing the speed of execution to the number of the eigenvectors. This new methodology is faster than the previous algorithm developed by the authors and all eigenvectors can be obtained with it. In addition, the performance using the Coope matrix has been tested contrasting the results with another technique published in the scientific literature.
It is generally assumed in dynamic positioning of over-actuated marine vessels that the control effectiveness matrix (input matrix) is known and constant, or, in case of fault information, it is estimated by the fault detection and diagnosis system. The purpose of the study is to develop the adaptive dynamic positioning control system for an over-actuated marine vessel in the presence of uncertainties and with emphasis on limited information about thruster forces. The proposed approach bases on the MIMO adaptive backstepping method to design the high-level control law and then to give inputs to the control allocation unit. An adaptive solution allows to accommodate the unknown time-varying control effectiveness matrix and to update the thrust distribution due to actuator losses and failures. The effectiveness and correctness of the proposed control schema is demonstrated by simulations involving a redundant set of actuators when some of them have lost partially their efficiency or failed. The evaluation criteria include energy consumption, robustness and accuracy of dynamic positioning during typical vessel operations. Based on simulation tests results, the generated control inputs stabilize the ship position and orientation violated by thruster faults.
The aim of this study is to investigate the numerical treatment of the Painlevé equation-II arising in physical models of nonlinear optics through artificial intelligence procedures by incorporating a single layer structure of neural networks optimized with genetic algorithms, sequential quadratic programming and active set techniques. We constructed a mathematical model for the nonlinear Painlevé equation-II with the help of networks by defining an error-based cost function in mean square sense. The performance of the proposed technique is validated through statistical analyses by means of the one-way ANOVA test conducted on a dataset generated by a large number of independent runs.
In this study a novel application of neurocomputing technique is presented for nonlinear fluid mechanics problem arising in the model of the flow over stretchable rotating disk in the presence of strong magnetic field. The scheme comprises of the power of effective modelling of neural networks supported with integrated optimization strength of genetic algorithm and interior-point method. The governing partial differential equation of the system is converted to nonlinear systems of simultaneous ordinary differential equations by incorporating the similarity variables. Neural network based approximate differential equation models are formulated for the transformed system that are used to construct the merit function in mean squared error sense. The networks are trained initially by genetic algorithm for the global search and rapid local refinements is attained through efficient interior point method. The given scheme is applied for dynamical analysis of the system model in terms of radial, tangential, axial velocities and heat effects by varying magnetic interaction parameters, unsteadiness factors, disk stretchable magnitudes, and Prandtl numbers. The statistical performance indices based on error from standard numerical solutions are used to validate the correctness, consistency, robustness and stability of the proposed stochastic solver.
A neuro-heuristic scheme is design to solve nonlinear singular second order system based on Thomas-Fermi equation using the strength of universal approximation capabilities of feedforward artificial neural networks supported with optimization power of genetic algorithms and sequential quadratic programming. An error function is constructed by differential equations artificial neural networks and optimization of design parameters of networks is carried out initially with genetic algorithms for the global search while sequential quadratic programming algorithm is used for further rapid local refinements. The performance of the design is analyzed by solving variants of Thomas-Fermi equation. Comparison of the results with standard numerical as well as analytical solvers establish the significance of the method on the basis of accuracy and convergence through statistical performance indices.
A community structure is an integral part of a social network. Detecting such communities plays an important role in a wide range of applications, including but not limited to, cluster analysis, recommendation systems and understanding the behavior of complex systems. Researchers have derived many algorithms to discover the community structures of networks. Discovering communities is a challenging task, and there is no single algorithm that produces the best results for all networks. Therefore, despite many elegant solutions, discovering communities remains an active area of research. In this paper, we propose a novel algorithm, the Clustering Coefficient-based Genetic Algorithm (CC-GA), for detecting them in social and complex networks. Researchers have used several genetic algorithms to detect communities, but the proposed algorithm is novel in terms of both the generation of the initial population and the mutation method, and thus improve its efficiency and accuracy. Experiments on a variety of real-world datasets and a comparison to state-of-the-art genetic and non-genetic-based algorithms show improved results. We have made the source code available at (https://github.com/Anwar-Said/CC-GA) for foster reproducibility research.
In this study, bio-inspired computing is presented for finding an approximate solution of governing system represents the dynamics of the HeartBeat Model (HBM) using feed-forward Artificial Neural Networks (ANNs), optimized with Genetic Algorithms (GAs) hybridized with Interiort-Point Algorithm (IPA). The modeling of the system is performed with ANNs by defining an unsupervised error function and optimization of unknown weights are carried out with GA-IPA; in which, GAs is used as an effective global search method and IPA for rapid local convergence. Design scheme is applied to study the dynamics of HBM by taking different values for perturbation factor, tension factor in the muscle fiber and the length of the muscle fiber in the diastolic state. A large number of simulations are performed for the proposed scheme to determine its effectiveness and reliability through different performance indices based on mean absolute deviation, Nash-Sutcliffe efficiency, and Thiel's inequality coefficient.
In this paper, a new method based on single layer Legendre Neural Network (LeNN) model has been developed to solve initial and boundary value problems. In the proposed approach a Legendre polynomial based Functional Link Artificial Neural Network (FLANN) is developed. Nonlinear singular initial value problem (IVP), boundary value problem (BVP) and system of coupled ordinary differential equations are solved by the proposed approach to show the reliability of the method. The hidden layer is eliminated by expanding the input pattern using Legendre polynomials. Error back propagation algorithm is used for updating the network parameters (weights). Results obtained are compared with the existing methods and are found to be in good agreement.
In this study, stochastic numerical treatment is presented for boundary value problems (BVPs) arising in nanofluidics for nonlinear Jeffery-Hamel flow (NJ-HF) equations using feed-forward artificial neural networks (ANNs) optimized with bio-inspired computing based on genetic algorithms (GAs) integrated with the active-set method (ASM). NJ-HF equations associated with both convergent and divergent channels, involving nanoparticles, are derived from the transformation of Navier-Stokes partial differential equations to nonlinear BVPs of third-order ordinary differential equations. The mathematical model of the transformed BVPs is developed with the help of ANNs in an unsupervised manner and the design parameters of these networks are trained with GAs, ASM, and GA-ASM. The design scheme is evaluated for NJ-HF by taking water as a base fluid containing three different types of nanomaterials: copper (Cu), alumina (Al2O3), and titania (TiO2) under various scenarios based on the angle of the channels and Reynolds numbers. Accuracy and convergence of the designed scheme are validated through comparison with standard numerical results using the Adams method.
For periodic gait optimization problem of the bipedal walking robot, a class of global and feasible sequential quadratic programming algorithm (FSQPA) is proposed based on discrete mechanics and optimal control. The optimal controls and trajectories are solved by the modified FSQPA. The algorithm can rapidly converge to a stable gait cycle by selecting an appropriate initial gait; otherwise, the algorithm only needs one step correction that generates a stable gait cycle. Under appropriate conditions, we provide a rigorous proof of global convergence and well-defined properties for the FSQPA. Numerical results show that the algorithm is feasible and effective. Meanwhile, it reveals the movement mechanism in the process of bipedal dynamic walking, which is the velocity oscillations. Furthermore, we overcome the oscillatory behavior via the FSQPA, which makes the bipedal robot walk efficiently and stably on even terrain. The main result is illustrated on a hybrid model of a compass-like robot through simulations and is utilized to achieve bipedal locomotion via FSQPA. To demonstrate the effectiveness of the high-dimensional bipedal robot systems, we will conduct numerical simulations on the model of RABBIT with nonlinear, hybrid, and underactuated dynamics. Numerical simulation results show that the FSQPA is feasible and effective. Copyright
In this paper, the homotopy analysis method is used for solving a prey-predator system with holling IV functional response. The approximation solutions were obtained by homotopy analysis method, and contain the auxiliary parameter h which provides us with a convenient way to adjust and control convergence region and rate of solution series. This result showed that this method is valid and feasible for the system.
In the present study, a new soft computing framework is developed for solving nanofluidic problems based on fluid flow and heat transfer of Multi-Walled Carbon Nanotube (MWCNT) along a flat plate with Navier slip boundary with the help of Artificial Neural Networks (ANNs), Genetic Algorithms (GAs), Interior-Point Algorithm (IPA) and hybridized approach GA-IPA. Original PDEs associated with the problem are transformed into system of nonlinear ODEs using similarity transformation. Mathematical model of transformed system is constructed by exploiting the strength of universal function approximation ability of ANNs and an unsupervised error function is formulated for the system in a least mean square sense. Learning of the design variable of the networks is carried out with GAs supported with IPA for rapid local convergence. The design scheme is applied to solve number of variants by taking water, engine oil and kerosene oil as a base fluids mixed with different concentrations of MWCNTs. The reliability and effectiveness of the design scheme is measured with the help of results of statistical analysis based on sufficient large number of independent runs of the algorithms rather than single successful run. The comparative studies of the proposed solution are made with standard numerical results in order to establish the correctness of the given scheme.
In the present article, a relatively very new technique viz. Coupled Fractional Reduced Differential Transform, has been executed to attain the approximate numerical solution of the predator-prey dynamical system. The fractional derivatives are defined in the Caputo sense. Utilizing the present method we can solve many linear and nonlinear coupled fractional differential equations. The results thus obtained are compared with those of other available methods. Numerical solutions are presented graphically to show the simplicity and authenticity of the method.
In this research, the well-known non-linear Lane–Emden–Fowler (LEF) equations are approximated by
developing a nature-inspired stochastic computational intelligence algorithm. A trial solution of the model
is formulated as an artificial feed-forward neural network model containing unknown adjustable parameters.
From the LEF equation and its initial conditions, an energy function is constructed that is used in
the algorithm for the optimisation of the networks in an unsupervised way. The proposed scheme is tested
successfully by applying it on various test cases of initial value problems of LEF equations. The reliability
and effectiveness of the scheme are validated through comprehensive statistical analysis. The obtained
numerical results are in a good agreement with their corresponding exact solutions, which confirms the
enhancement made by the proposed approach.