Ernesto Zambrano-Serrano

Autonomous University of Nuevo León | UANL · Facultad de Ingeniería Mecánica y Eléctrica

The fifth edition of the Meeting for the Dissemination and Research in the Study of Complex Systems and their Applications (EDIESCA 2024, for its meaning in Spanish), will be held in a hybrid modality (virtual, and face-to-face), during October 28-30, having as headquarters the facilities of the Universidad Panamericana Campus Aguascalientes. EDIES...

This study employs an approach that centers on the utilization of support vector machine classifiers to categorize chaotic dynamics. Commonly, within chaotic secure communication schemes, one state variable of a determined dynamical system is employed for encrypting information, while another operates as the cryptographic key. Successful communicat...

Variable-order fractional derivatives can be considered as a natural and analytical extension of constant fractional-order derivatives. In variable-order derivatives, the order can vary continuously as a function of either dependent or independent variables of differentiation, such as time, space, or even independent external variables. The main co...

Understanding the dynamics of complex systems defined in the sense of Caputo, such as fractional differences, is crucial for predicting their behavior and improving their functionality. In this paper, the emergence of chaos in complex dynamical networks with indirect coupling and discrete systems, both utilizing fractional order, is presented. The...

On behalf of the Organizing Committee of the 4th Meeting for the Dissemination and Research in the Study of Complex Systems and their Applications (EDIESCA 2023, for its meaning in Spanish), I would like to cordially invite you and your students to participate as guests speakers and take part in the event, that will be held in a hybrid modality (vi...

This paper presents a methodology to obtain the Fourier coefficients (FCs) and the derivative Fourier coefficients (DFCs) from an input signal. Based on the Taylor series that approximates the input signal into a trigonometric signal model through the Kalman filter, consequently, the signal’s and successive derivatives’ coefficients are obtained wi...

This paper presents a chaotic map's fractionalization, dynamical analysis, control, and synchronization in a leader-follower configuration. The fractional-order version of the chaotic map is obtained based on the Caputo-like delta difference operator. Then, the dynamical behaviors associated with the fractional-order difference system are analyzed...

This work presents a numerical analysis of the dynamical behavior of a multi-scroll chaotic system using variable-order calculus. In this scenario, we introduce the concept of variable-order from two approaches denominated herein as short-memory and full-memory, respectively. For the first one, the basic idea is to study the chaotic dynamics when t...

This article is devoted to the determination of numerical solutions for the two-dimensional time–spacefractional Schrödinger equation. To do this, the unknown parameters are obtained using the Laguerre wavelet approach. We discretize the problem by using this technique. Then, we solve the discretized nonlinear problem by means of a collocation meth...

The research related to complex networks is an active field mainly inspired by its broad ability to model a wide variety of systems. For instance, we observe biological networks at the microscopic level, genetic regulation networks, protein networks, and neural networks. On the other hand, we find computer networks and social networks at a higher l...

Dear Colleagues, Nonlinear dynamics is a useful tool in the mathematical modelling of various systems, such as electronic devices, economies, and physical processes, to mention a few. Nonlinear dynamics has had a great impact on areas of scientific research ranging from chemistry to physics and biology. Many nonlinear dynamics studies directed to t...

Since the variable-order fractional systems show more complex characteristics and more degrees of freedom due to time-varying fractional derivatives, we introduce a variable-order fractional Hopfield-like neural network in this paper. First, the properties and dynamical behavior of the system are studied. The variable-order derivative’s effects on...

In the human glucose-insulin regulatory system, diverse metabolic issues can arise, including diabetes type I and type II, hyperinsulinemia, hypoglycemia, etc. Therefore, the analysis and characterization of such a biological system is a must. It is well known that mathematical models are an excellent option to study and predict natural phenomena t...

When the bursting electrical activity (BEA) of the \(\beta \)-cells inside Langerhans’ islet behave synchronously, the insulin secretes into the bloodstream to regulate the body’s glucose levels. Recent advances in pancreas imaging techniques showed that the communication path among \(\beta \)-cells exhibits a small-world-like organization. Hence,...

In this paper, the trajectory tracking control and the field programmable gate array (FPGA) implementation between a recurrent neural network with time delay and a chaotic system are presented. The tracking error is globally asymptotically stabilized by means of a control law generated from the Lyapunov–Krasovskii and Lur’e theory. The applicabilit...

En este artículo, se presenta la ecuación diferencial fraccionaria de un circuito electrónico RC en términos de la derivada fraccionaria de tipo Caputo y la solución analítica exacta usando propiedades de la transformada de Laplace y la función Mittag-Leffler. El orden de la derivada fraccionaria es definido en el intervalo 0<q≤1, preservando la di...

In the present study, a new neural network-based terminal sliding mode technique is proposed to stabilize and synchronize fractional-order chaotic ecological systems in finite-time. The Chebyshev neural network is implemented to estimate unknown functions of the system. Moreover, through the proposed Chebyshev neural network observer, the effects o...

Because one of the main applications of chaos synchronization is oriented to data encryption and random number generators, fractional-order chaotic systems showing multi-scroll attractors have pointed out as feasible solutions to improve the performance of secure communications schemes. Nowadays, recent works have reported the analysis and control...

In this paper, by considering the Caputo-like delta difference definition, a fractional difference order map with chaotic dynamics and with no equilibria is proposed. The complex dynamical behaviors associated with fractional difference order maps are analyzed employing the phase portraits, bifurcations diagrams, and Lyapunov exponents. The complex...

We propose a novel chaotic oscillator derived from the generic four-dimensional autonomous jerk systems. By using the Routh–Hurwitz criterion, we analyze the equilibrium point stability. Furthermore, we use the bifurcation diagram and Lyapunov exponents to explore the chaotic regions of the oscillator. One of the novel hyperjerk systems’ main featu...

In this novel research, through dynamical analysis, we introduce for the first time a fractional-calculus based artificial macroeconomic model, actually implemented in the Laboratory via a new hardware set up. Firstly, we propose a new model of a discrete-time macroeconomic system where fractional derivatives are incorporated into the system of equ...

In this paper, an encryption, compression and transmission scheme is proposed. The scheme is based on fractional-order chaotic systems combined with Discrete Wavelet Transform (DWT) and Quadrature Phase Shift Keying (QPSK) modulation. The cipher performs rounds of digital operations between the vector states of the fractional-order system and the i...

For studying biological conditions with higher precision, the memory characteristics defined by the fractional-order versions of living dynamical systems have been pointed out as a meaningful approach. Therefore, we analyze the dynamics of a glucose-insulin regulatory system by applying a non-local fractional operator in order to represent the memo...

Considerado como el cuarto elemento pasivo en la teoría de circuitos, un memristor puede ser utilizado para diseñar sistemas caóticos e incrementar su complejidad. En este artículo se presenta la generación de atractores autoexcitados, coexistentes y ocultos. Las diferentes familias de atractores se generan al agregar la función no lineal de un mem...

Ad Hoc networks are considered essential elements of the Internet of Things (IoT), which is a technological trend for innovative future applications. Since in IoT systems the devices are mostly connected among them, the data exchange is a vital activity in the network. In this kind of networks, not only non-sensitive data exchange is performed, but...

A fractional-order finance system with negative values for system’s parameters is introduced. Based on an integer-order finance system with two nonlinearities, we discovered chaos in new regions for system’s parameters. By selecting negative values for system’s parameters, the eigenvalues of the proposed system can be modified to decrease the fract...

β-cells in the pancreas can be described by a model of coupled biological oscillators with communication links, which can synchronize their electrical activities, giving rise to a square-wave bursting-like insulin release. In fact, β-cells play a vital role in analyzing and characterizing diabetes conditions. This research work studies the synchron...

A novel fractional order dynamical system with a variable double-scroll attractor on a line, lattice and 3D grid is introduced. This system belongs to a class of chaotic systems with adjustable variables but with fractional order. Chaos generation only depends on the value of fractional order. As a result, a chaotic attractor is discovered and prop...

In this work, a new fractional-order chaotic system with a single parameter and four nonlinearities is introduced. One striking feature is that by varying the system parameter, the fractional-order system generates several complex dynamics: self-excited attractors, hidden attractors, and the coexistence of hidden attractors. In the family of self-e...

A double-scroll chaotic attractor generated by a fractional-order switched system is presented. Based on unstable dissipative systems (UDS) and a switching law, a fractional-order UDS is proposed. Chaos behavior is found with a fractional order as low as 2.568 by satisfying the stability criterion for fractional order chaotic systems. The fractiona...

In 1695, G. Leibniz laid the foundations of fractional calculus, but mathematicians revived it only 300 years later. In 1971, L.O. Chua postulated the existence of a fourth circuit element, called memristor, but Williams’s group of HP Labs realized it only 37 years later. In recent years, few unusual dynamical systems, such as those with a line of...

The analysis and simulation of nonlinear dynamical behavior of a biological system emulating a beta-cell are presented in this chapter. Based on the dynamical system described by three coupled nonlinear differential equations, the typical electrophysiology of an active beta-cell, known as Bursting Electrical Activity (BEA) or squared bursting can b...

In this paper, a new model based on piecewise linear (PWL) functions is proposed and analyzed by considering the well known Pernarowski's mathematical model for an isolated beta cell. Contrary to Pernarowski's model, we replace the original cubic functions with PWL functions with multi-segments in order to obtain bursting electrical activity (BEA)...

The analysis, design and circuit synthesis of a fractional order switched system is presented in this paper. That system is capable of showing chaotic oscillations with a fractional order less than three, i.e., 2.4. The dynamical system is called fractional order unstable dissipative system (FOUDS); because it consists of a switching law to display...

Resumen—Las células beta pancreáticas se encuentran agru-padas en los islotes de Langerhans y son las encargadas de producir y segregar insulina cuando su potencial de membrana se sincroniza en una dinámica no lineal denominada bursting. Por lo tanto en este trabajo se diseñadise˜diseña una red compleja del tipo mundo pequeñopeque˜pequeño para sinc...

Chaos generation in a new fractional order unstable dissipative system with only two equilibrium points is reported. Based on the integer version of an unstable dissipative system (UDS) and using the same system’s parameters, chaos behavior is observed with an order less than three, i.e., 2.85. The fractional order can be decreased as low as 2.4 va...

In this chapter, the guidelines to synchronize one-directional (1D) and two-directional (2D) multi-scroll chaos generators by means of Generalized Hamiltonian forms are presented. First, the multi-scroll chaotic oscillator is simulated at the electronic system level by applying state-variables and piecewise-linear approaches. Besides, we apply scal...

We study the synchronization of a piecewise linear function-based chaotic system. That system generates multiple scrolls in multiple directions (two- and three-directions) on phase space. In this scenario, the design of a controller based on Generalized Hamiltonian forms is possible. As function of control signals, we propose a master–slave synchro...

In this paper, a study of the effects on using a different number of control signals in the synchronization of multi-directional multi-scroll chaos generators is presented. We adopt Generalized Hamiltonian forms approach to synchronize two 3D multi-scroll chaotic attractors. First, it is used only one state-variable (x, y, z) from the master system...

In this paper, a chaotic synchronization scheme for multi-directional multi-scroll chaos generators is presented. We use Generalized Hamiltonian forms approach to determine the synchronization conditions for two unidirectionally coupled multi-directional multi-scroll chaotic attractors. First, two state variables of the master system are used to co...