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(color online) Equivalent phase portraits by Chua's chaotic circuit with two output differentiators with (a) R = 2.0 kΩ and (b) R = 2.4 kΩ.
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A novel mapping equivalent approach is proposed in this paper, which can be used for analyzing and realizing a memristor-based dynamical circuit equivalently by a nonlinear dynamical circuit with the same topologies and circuit parameters. A memristor-based chaotic circuit and the corresponding Chua's chaotic circuit with two output differentiators...
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... comparing Fig. 6 with Fig. 4, it can be found that the output voltages of Chua's chaotic circuit via two output differentiators and the memristor-based chaotic circuit have the similar dynamical characteristics, which verify that the mapping equivalent approach is effective for the equiva- lent analysis of the memristor-based chaotic circuit by utiliz- ...
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Citations
... In sensing, memristors can be used to detect changes in electrical signals, which has applications in areas such as biosensing and environmental monitoring. In energy storage, memristors can be used to store energy, which has potential applications in areas such as renewable energy systems and electric vehicles [3,8,[13][14][15][16]. ...
Memristors are a type of electronic circuit element that was first proposed in the early 1970s. Unlike traditional circuit elements such as resistors, capacitors, and inductors, memristors has last memory and can therefore be used to store information. They were initially considered a theoretical concept, but recent advances in nanotechnology have made it possible to create physical memristor devices and apply it in various aspect of life. Memristors are considered the fourth fundamental circuit element, alongside resistors, capacitors, and inductors. They have unique properties, such as the ability to store information in their resistance state, which makes them promising candidates for future computing systems. Memristors have been integrated into crossbar arrays, which allow for massively parallel computing with low power consumption. Memristor fabrication methods vary based on the materials used and the intended application. Thin-film deposition, nanoimprint lithography, and self-assembly processes are common techniques. The performance properties of the memristor, such as switching speed, endurance, and scalability, are influenced by the material selection, such as polymers or transition metal oxides. Memristors have a wide range of potential applications, including in the development of artificial intelligence and neural networks. They can also be used in memory devices, logic circuits, and sensor applications. Research is ongoing to further explore the unique properties of this lovely device and to develop various applications for it. The unique properties of memristors have also sparked interest in unconventional computing paradigms. Memristor-based systems have shown potential for implementing neural networks, cellular automata, and even analog computers, providing alternative approaches to solving complex computational problems. Memristor-based logic and arithmetic units offer advantages in terms of power efficiency and density compared to traditional transistor-based designs. This project shows the progress made in memristor technology, including the development of various memristive materials and device architectures. It explores the challenges associated with memristor fabrication, reliability, and scalability. Moreover, the paper highlights recent advancements in memristor-based applications, such as in-memory computing, deep learning accelerators, and brain-inspired computing systems. This piece provides an overview of the theory behind memristors, including their mathematical models and properties. It also discusses the different types of memristor devices that have been developed and their potential applications. Finally, it highlights some of the challenges and future directions in the field of memristor research.
... Luo et al. [21] developed an application of a memristor-based oscillator to weak signal detection. In order to study the influence of the delay on the dynamic of the memristive system, Ding et al. [22] studied the chaos and Hopf bifurcation control in a fractional-order memristor-based chaotic system with time delay while Bao et al. [23], developed a memristor oscillation circuit based on two memristors and the mapping equivalent approach to the analysis and realization of memristor-based dynamical circuit was presented by the same authors [24]. Pu and Yuan [25] reported the fracmemristor: Fractionalorder memristor in which they initiated an interesting conceptual framework of fracmemristor. ...
In this research work, we propose to investigate the effect of fractional-order on the dynamics of a four dimensional (4D) chaotic system by adding a new model of a memristor, which is an essential electronic element with interesting applications. First introduced by Li et al. (Int J Circuit Theory Appl 42(11):1172–1188, 2014, https://doi.org/10.1002/cta.1912), the original system is investigated prior to the more detailed study by Pham et al., The system is found to be self-excited, has a line of equilibrium which are all unstable with regards to the stability condition of fractional-order systems. The bifurcation tools associated with lyapunov exponents reveal the rich dynamics behavior of the proposed system. Our analysis shows that the degree of complexity of the system increases as the fractional-order decreases from 1 to 0.97. Of most/particuar interest, an analog electronic circuit is designed and implemented in PSPICE for verification and confirmed by laboratory experimental measurements. Finally, an ARM-FPGA-based implementation of the 4D fractional-order chaotic system is presented in this work to illustrate the performance of the proposed scheme.
... In this study, we added a fourth passive component with improved nonlinear characteristics. We shall introduce the memristor W(φ) , a component made up of an electrical charge (q) and a magnetic flux ( φ ) that has been physically achieved by Stanley William's team at HP labs [41][42][43][44][45][46][47] . Herein, the smooth cubic flux-controlled memristor is hereby characterized by a smooth continuous cubic nonlinearity given by 12 where β and ξ are parameters embedded in the memristive-based function, φ is the internal state variable of W(φ) . ...
In-depth analysis of a novel multiple scroll memristive-based hyperchaotic system with no equilibrium is provided in this work. We identify a family of more complicated nth\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\mathrm{th}$$\end{document}-order multiple scroll hidden attractors for a unique, enhanced 4-dimensional Sprott-A system. The system is particularly sensitive to initial conditions with coexistence and multistability of attractors when changing the associated parameters and the finite transient simulation time. The complexity (CO), spectral entropy (SE) algorithms, and 0-1 complexity characteristics was thoroughly discussed. On the other hand, the outcomes of the electronic simulation are validated by theoretical calculations and numerical simulations.
... The MHSO is achieved in figure 1. Figure 1 is realized by introducing a no-defect and intense flux-controlled memristor [39,40] to the schematic of a self-driven Helmholtz jerk circuit [38]. The designed schematic of figure 1 is composed of 5 operational amplifiers (OPAM), 10 resistors, 1 analog multiplier, 3 capacitors, and a no-defect and intense fluxcontrolled memristor. ...
... The designed schematic of figure 1 is composed of 5 operational amplifiers (OPAM), 10 resistors, 1 analog multiplier, 3 capacitors, and a no-defect and intense fluxcontrolled memristor. Depicting from the schematic of the no defect and intense flux-controlled memristor possessing a pure memristance function as in [39][40][41][42] is captured in figure 1. Hence the expression of the memductance is given by: ...
This paper explores the dynamics and electronic validations of a memristive Helmholtz snap oscillator (MHSO), employing it to model a process of pseudo-random number generator (PRNG). The MHSO depicts two lines of equilibrium points. Characterizing the stability of the equilibrium domains, Hopf bifurcation is associated with one of the equilibrium domains while the other region of equilibrium points is always unstable. Extreme multistability features, hidden complex attractors, antimonotonicity, period-3-oscillations and complex hidden attractors coexisting, chaotic bubbles, and hidden attractors are generated in MHSO for particular values of parameters. Electronic validations of MHSO based on OrCAD-PSpice software and microcontroller reveal that OrCAD-PSpice and microcontroller dynamics agree well with the dynamics achieved by numerical simulations. Lastly, the chaotic characteristics depicted by the MHSO are used to design a process of PRNG. The generated random bits are validated successfully by a standard statistical tool set by the National Institute of Standards and Technology (NIST-800-22).
... (1) In some practical systems, there are components with piecewise linear characteristics [1][2][3]. For example, paper [1] studies a robust control problem for a memristor loop with piecewise linear properties; literature [2] studies a NASA aerospace vehicle test system with piecewise linear properties and a piecewise linear mechanical system et al [3]. ...
... (1) In some practical systems, there are components with piecewise linear characteristics [1][2][3]. For example, paper [1] studies a robust control problem for a memristor loop with piecewise linear properties; literature [2] studies a NASA aerospace vehicle test system with piecewise linear properties and a piecewise linear mechanical system et al [3]. ...
In this paper, we mainly study the output feedback control problem of stochastic nonlinear system based on loose growth conditions and applies the research results to the electric vehicle control system of underwater oil and gas pipelines, which can improve the speed and stability of the equipment system. Firstly, the concept of randomness is introduced to study the tracking control problem of the system, which meet the more general polynomial function growth conditions. A combination of static and dynamic output feedback practices is proposed. The tracking controller makes all the states of the system, which meet boundedness and ensures that the tracking error of the system converges to a small neighborhood of zero. Secondly, the system is extended to the parameter uncertain system, the controller with complete dynamic gain is constructed by proving the boundedness of the system state and gain. Furtherly, the nonlinear term of the system satisfies the more relaxed power growth condition, combined with the inverse method to construct a set of Lyapunov functions and obtain the controller to ensure that the system is asymptotically probabilistic stability in the global scope. Finally, through the ocean library in the Simulation X software, the controller design results are imported into the underwater electro-hydraulic actuator model to verify the effectiveness.
... With the development of science and technology, ocean exploration technology has reached an unprecedented new level. With the help of science and technology, AUVs have been developed [1,2]. It is now possible to conduct scientific investigations on the seabed at a depth of 10,000 m. ...
... The literature researches the AUV's velocity, which isl = (ẋ 2 +ẏ 2 +ż 2 ) 1 2 . Considering the system origin stations, 1 ...
... Well-known α 1 l [1] is a series of controller, which is virtual and step designed. ...
In this paper, an underwater robot system with nonlinear characteristics is studied by a backstepping method. Based on the state preservation problem of an Autonomous Underwater Vehicle (AUV), this paper applies the backstepping probabilistic gain controller to the nonlinear system of the AUV for the first time. Under the comprehensive influence of underwater resistance, turbulence, and driving force, the motion of the AUV has strong coupling, strong nonlinearity, and an unpredictable state. At this time, the system’s output feedback can solve the problem of an unmeasurable state. In order to achieve a good control effect and extend the cruising range of the AUV, first, this paper will select the state error to make it a new control objective. The system’s control is transformed into the selection of system parameters, which greatly simplifies the degree of calculation. Second, this paper introduces the concept of a stochastic backstepping control strategy, in which the robot’s actuators work discontinuously. The actuator works only when there is a random disturbance, and the control effect is not diminished. Finally, the backstepping probabilistic gain controller is designed according to the nonlinear system applied to the simulation model for verification, and the final result confirms the effect of the controller design.
... (1) Different from the research object in [13][14][15][16], the state equation of the control object we studied in this chapter contains both a time-delay term and an uncertain parameter, including a nonlinear function term of the state and time delay. Among them, the uncertainty includes the uncertainty of the state and time delay, the uncertainty of the disturbance, and the uncertainty of the Hölder condition nonlinear function. ...
This paper mainly studies the output feedback control problem of the stochastic nonlinear system based on loose growth conditions and applies the research results to the valve control system of underwater oil and gas pipelines, which can improve the speed and stability of the equipment system. First, the concept of randomness is introduced to study the actual tracking control problem of output feedback of stochastic nonlinear systems, remove the original harsher growth conditions, make it meet the more general polynomial function growth conditions, and propose a combination of static and dynamic output feedback practices. The design of the tracking controller makes all the states of the system meet boundedness and ensures that the tracking error of the system converges to a small neighborhood of zero. Second, the system is extended to the parameter-uncertain system, and the output feedback tracking controller with complete dynamic gain is constructed by proving the boundedness of the system state and gain. Further, the time-delay factor is introduced, and the nonlinear term of the system satisfies the more relaxed power growth condition, combined with the inverse method to cleverly construct a set of Lyapunov functions and obtain the output controller to ensure that the system is asymptotically probabilistic in the global scope. Stability. Finally, through the ocean library in the Simulation X simulation software, the controller design results are imported into the underwater electro-hydraulic actuator model to verify the effectiveness of the controller design.
... Bao et al. [23] built the reduce-ordered flux-charge model of a two-memristor-based circuit and analyzed its dynamical characteristics via the voltage-current and fluxcharge models. Bao et al. [24] qualitatively pointed out that the flux-charge model of the memristive circuit can be equivalent to realize its dynamical behavior in the voltagecurrent model. However, in these early studies, the state initials of the memristive circuit were not explicitly expressed in the dimensionality reduction model [25], resulting in the information loss of state initials of the memristive circuit. ...
... erefore, in the process of analyzing the multistability of the memristive circuit and system, in order to solve these problems, researchers proposed different dimensionality reduction modeling schemes based on the memristive circuit [20] and memristive system [21]. In fact, a prototype of dimensionality reduction modeling had been developed in the earlier literature [22][23][24]. In [22], the concept of dimensionality reduction modeling was proposed, which modeled the memristive circuits with two physical quantities of flux and charge as main state variables, and the dimension of the obtained flux-charge model was lower than that of the traditional voltage-current model. ...
... Bao et al. [23] built the reduce-ordered flux-charge model of a two-memristorbased memristive circuit and analyzed its dynamical characteristics via the voltage-current and flux-charge models. Bao et al. [24] qualitatively pointed out that the flux-charge model of the memristive circuit could be equivalent to realize its dynamical behavior in the voltage-current model. However, in these early studies, the state initials of the memristive circuits were not explicitly expressed in the dimensionality reduction model [25], resulting in the information loss of state initials of the memristive circuit. ...
Due to the introduction of memristors, the memristor-based nonlinear oscillator circuits readily present the state initial-dependent multistability (or extreme multistability), i.e., coexisting multiple attractors (or coexisting infinitely many attractors). The dimensionality reduction modeling for a memristive circuit is carried out to realize accurate prediction, quantitative analysis, and physical control of its multistability, which has become one of the hottest research topics in the field of information science. Based on these considerations, this paper briefly reviews the specific multistability phenomenon generating from the memristive circuit in the voltage-current domain and expounds the multistability control strategy. Then, this paper introduces the accurate flux-charge constitutive relation of memristors. Afterwards, the dimensionality reduction modeling method of the memristive circuits, i.e., the incremental flux-charge analysis method, is emphatically introduced, whose core idea is to implement the explicit expressions of the initial conditions in the flux-charge model and to discuss the feasibility and effectiveness of the multistability reconstitution of the memristive circuits using their flux-charge models. Furthermore, the incremental integral transformation method for modeling of the memristive system is reviewed by following the idea of the incremental flux-charge analysis method. The theory and application promotion of the dimensionality reduction modeling and multistability reconstitution are proceeded, and the application prospect is prospected by taking the synchronization application of the memristor-coupled system as an example.
... (corresponding author) ing memories [16], memristor cellular [17], or programmable analog integrated circuits [18]. Rich dynamical behaviors leading to striking applications with memristive based systems [19][20][21] have been discovered. Recently, Kuznetsov et al. introduced a new classification of attractors generated by nonlinear dynamics namely self-excited attractors and hidden attractors [23][24][25][26]. ...
... This is what guides us to propose a novel circuit. We consider the same original circuit used in [50] and replace the cubic power symmetrical nonlinearity with a flux controlled memristor, since a memristor has an impressive advantage to enlarge the dynamics of a given system with rich phenomena [19][20][21][22]. ...
This paper presents a novel fourth-order autonomous flux controlled memristive Wien-bridge system. Standard nonlinear diagnostic tools such as bifurcation diagram, graphs of largest Lyapunov exponent, Lyapunov stability diagram, phase space trajectory and isospike diagram are used to characterize dynamics of the system.
Results show that the system presents hidden attractors with infinite equilibrium points known as line equilibrium for a suitable set of its parameters. The system also exhibits striking phenomenon of extreme multistability. Through isospike and Lyapunov stability diagram, spiral bifurcation leading to a center hub point is observed in a Wien-bridge circuit for the first time and the Field Programmable Gate Array -based implementation is performed to confirm its feasibility.
... Output tracking control is an important topic in control theory. It has received extensive attention in the recent decades [13][14][15]. Under some strong conditions imposed on the system and the tracked signal, the asymptotic stabilization implies the asymptotic tracking problem. ...
This paper mainly focuses on the output practical tracking controller design for a class of complex stochastic nonlinear systems with unknown control coefficients. In the existing research results, most of the complex systems are controlled in a certain direction, which leads to the disconnection between theoretical results and practical applications. The authors introduce unknown control coefficients, and the values of the upper and lower bounds of the control coefficients are generalized by constants to allow arbitrary values to be arbitrarily large or arbitrarily small. In the control design program, the design problem of the controller is transformed into a parameter construction problem by introducing appropriate coordinate transformation. Moreover, we construct an output feedback practical tracking controller based on the dynamic and static phase combined by Ito stochastic differential theory and selection of appropriate design parameters, ensuring that the system tracking error can be made arbitrarily small after some large enough time. Finally, a simulation example is provided to illustrate the efficiency of the theoretical results.
