scholarly journals On a Memristor-Based Hyperchaotic Circuit in the Context of Nonlocal and Nonsingular Kernel Fractional Operator

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Shahram Rezapour ◽  
Chernet Tuge Deressa ◽  
Sina Etemad
Keyword(s):  
Fractional Order ◽  
Approximate Solutions ◽  
Order System ◽  
Banach Fixed Point Theorem ◽  
Dimensional System ◽  
Hyperchaotic System ◽  
Memory Element ◽  
Trivial Equilibrium ◽  
Uniqueness Of The Solution ◽  
Order Change

Memristor is a nonlinear and memory element that has a future of replacing resistors for nonlinear circuit computation. It exhibits complex properties such as chaos and hyperchaos. A five-dimensional memristor-based circuit in the context of a nonlocal and nonsingular fractional derivative is considered for analysis. The Banach fixed point theorem and contraction principle are utilized to verify the existence and uniqueness of the solution of the five-dimensional system. A numerical method developed by Toufik and Atangana is used to get approximate solutions of the system. Local stability analysis is examined using the Matignon fractional-order stability criteria, and it is shown that the trivial equilibrium point is unstable. The Lyapunov exponents for different fractional orders exposed that the nature of the five-dimensional fractional-order system is hyperchaotic. Bifurcation diagrams are obtained by varying the fractional order and two of the parameters in the model. It is shown using phase-space portraits and time-series orbit figures that the system is sensitive to derivative order change, parameter change, and small initial condition change. Master-slave synchronization of the hyperchaotic system was established, the error analysis was made, and the simulation results of the synchronized systems revealed a strong correlation among themselves.

Dynamical Analysis and Circuit Simulation of a New Fractional-Order Hyperchaotic System and Its Discretization

2016 ◽  
Vol 26 (13) ◽  
pp. 1650222 ◽  
Author(s):  
A. M. A. El-Sayed ◽  
A. Elsonbaty ◽  
A. A. Elsadany ◽  
A. E. Matouk
Keyword(s):  
Fractional Order ◽  
Initial Conditions ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Phase Portraits ◽  
Control Technique ◽  
Order System ◽  
Qualitative Behavior ◽  
Hyperchaotic System

This paper presents an analytical framework to investigate the dynamical behavior of a new fractional-order hyperchaotic circuit system. A sufficient condition for existence, uniqueness and continuous dependence on initial conditions of the solution of the proposed system is derived. The local stability of all the system’s equilibrium points are discussed using fractional Routh–Hurwitz test. Then the analytical conditions for the existence of a pitchfork bifurcation in this system with fractional-order parameter less than 1/3 are provided. Conditions for the existence of Hopf bifurcation in this system are also investigated. The dynamics of discretized form of our fractional-order hyperchaotic system are explored. Chaos control is also achieved in discretized system using delay feedback control technique. The numerical simulation are presented to confirm our theoretical analysis via phase portraits, bifurcation diagrams and Lyapunov exponents. A text encryption algorithm is presented based on the proposed fractional-order system. The results show that the new system exhibits a rich variety of dynamical behaviors such as limit cycles, chaos and transient phenomena where fractional-order derivative represents a key parameter in determining system qualitative behavior.

scholarly journals A No-Equilibrium Hyperchaotic System and Its Fractional-Order Form

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Duy Vo Hoang ◽  
Sifeu Takougang Kingni ◽  
Viet-Thanh Pham
Keyword(s):  
Fractional Order ◽  
Chaotic Behavior ◽  
Chaotic Attractors ◽  
Dimensional System ◽  
Hyperchaotic System ◽  
Equilibrium System ◽  
Coexisting Attractors ◽  
Amplitude Control ◽  
Dynamical Behaviors ◽  
Point Attractor

No-equilibrium system with chaotic behavior has attracted considerable attention recently because of its hidden attractor. We study a new four-dimensional system without equilibrium in this work. The new no-equilibrium system exhibits hyperchaos and coexisting attractors. Amplitude control feature of the system is also discovered. The commensurate fractional-order version of the proposed system is studied using numerical simulations. By tuning the commensurate fractional-order, the proposed system displays a wide variety of dynamical behaviors ranging from coexistence of quasiperiodic and chaotic attractors and bistable chaotic attractors to point attractor via transient chaos.

scholarly journals A New Fractional-Order Hyperchaotic System and Its Adaptive Tracking Control

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Yinlan Chen ◽  
Haodong Zhang ◽  
Xu Kong
Keyword(s):  
Fractional Order ◽  
Tracking Control ◽  
Dynamical Behavior ◽  
Order System ◽  
Periodic Signal ◽  
Heterogeneous Structure ◽  
Hyperchaotic System ◽  
Adaptive Tracking Control ◽  
Adaptive Tracking ◽  
Adaptive Control Strategy

We construct for the first time a fractional-order hyperchaotic system via the original integer-order system. The dynamical behavior of this fractional-order hyperchaotic system is investigated in detail using first approximation method and Lyapunov exponents. Next, an adaptive control strategy for the univariate controlled hyperchaotic system has been proposed. Also, the tracking performance is fully taken into account in numerous applications, for instance, tracking sinusoidal periodic signal, self-synchronization, and generalized synchronization of heterogeneous structure. Simulation results illustrate the validity and performability of the proposed adaptive tracking control scheme.

One-to-four-wing hyperchaotic fractional-order system and its circuit realization

Circuit World ◽  
2020 ◽  
Vol 46 (2) ◽  
pp. 107-115
Author(s):  
Xiang Li ◽  
Zhijun Li ◽  
Zihao Wen
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Complexity Analysis ◽  
Initial Conditions ◽  
Fractional Order System ◽  
Order System ◽  
Hyperchaotic System ◽  
Circuit Realization ◽  
Content Type

Purpose This paper aims to introduce a novel 4D hyperchaotic fractional-order system which can produce one-to-four-wing hyperchaotic attractors. In the study of chaotic systems with variable-wing attractors, although some chaotic systems can generate one-to-four-wing attractors, none of them are hyperchaotic attractors, which is incomplete for the dynamic characteristics of chaotic systems. Design/methodology/approach A novel 4D fractional-order hyperchaotic system is proposed based on the classical three-dimensional Lü system. The complex and abundant dynamic behaviors of the fractional-order system are analyzed by phase diagrams, bifurcation diagrams and the corresponding Lyapunov exponents. In addition, SE and C0 algorithms are used to analyze the complexity of the fractional-order system. Then, the influence of order q on the system is also investigated. Finally, the circuit is implemented using physical components. Findings The most particular interest is that the system can generate one-to-four-wing hyperchaotic attractors with only one parameter variation. Then, the hardware circuit experimental results tally with the numerical simulations, which proves the validity and feasibility of the fractional-order hyperchaotic system. Besides, under different initial conditions, coexisting attractors can be obtained by changing the parameter d or the order q. Then, the complexity analysis of the system shows that the fractional-order chaotic system has higher complexity than the corresponding integer-order chaotic system. Originality/value The circuit structure of the fractional-order hyperchaotic system is simple and easy to implement, and one-to-four-wing hyperchaotic attractors can be observed in the circuit. To the best of the knowledge, this unique phenomenon has not been reported in any literature. It is of great reference value to analysis and circuit realization of fractional-order chaotic systems.

A Fractional-Order Hyperchaotic System and its Circuit Implement

2014 ◽  
Vol 701-702 ◽  
pp. 1143-1147
Author(s):  
Qi Li Wang
Keyword(s):  
Fractional Order ◽  
Strange Attractor ◽  
Analog Circuit ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Order System ◽  
Hyperchaotic System ◽  
Dynamical Properties ◽  
Simulation Results ◽  
Sensitivity To Initial Conditions

A fractional-order hyperchaotic system was proposed and some basic dynamical properties were investigated to show chaotic behavior. These properties include instability of equilibria, sensitivity to initial conditions, strange attractor, Lyapunov exponents, and bifurcation. The fractional-order system presents hyperchaos, chaos, and periodic behavior when the parameters vary continuously. Then, an analog circuit is designed onMultisim 11and the Multisim results are agreed with the simulation results.

Chaos, Sliding Mode Control between Two Different Fractional-Order Hyperchaotic Systems with Uncertain Parameters

2012 ◽  
Vol 424-425 ◽  
pp. 318-323
Author(s):  
Hong Zhang ◽  
Dao Yin Qiu
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Control Method ◽  
Sliding Mode ◽  
Order System ◽  
Hyperchaotic System ◽  
Uncertain Parameters ◽  
Mode Control ◽  
Short Period ◽  
The Stability

This work investigates chaos synchronization between two different fractional-order hyperchaotic system (FOHS)s with uncertain parameters. The Chen FOHS is controlled to be synchronized with a new FOHS. The analytical conditions for the synchronization of different FOHSs are derived by utilizing the stability theory of fractional-order system. Furthermore, synchronization between two different FOHSs is achieved by utilizing sliding mode control method in a quite short period and both remain in chaotic states. Numerical simulations are used to verify the theoretical analysis using different values of the fractional-order parameter

scholarly journals On a new four-dimensional model of memristor-based chaotic circuit in the context of nonsingular Atangana–Baleanu–Caputo operators

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Chernet Tuge Deressa ◽  
Sina Etemad ◽  
Shahram Rezapour
Keyword(s):  
System Analysis ◽  
Phase Portraits ◽  
Banach Fixed Point Theorem ◽  
Memory Element ◽  
System A ◽  
Trivial Equilibrium ◽  
Computational Circuits ◽  
Parameter Values ◽  
The Given

AbstractA memristor is naturally a nonlinear and at the same time memory element that may substitute resistors for next-generation nonlinear computational circuits that can show complex behaviors including chaos. A four-dimensional memristor system with the Atangana–Baleanu fractional nonsingular operator in the sense of Caputo is investigated. The Banach fixed point theorem for contraction principle is used to verify the existence–uniqueness of the fractional representation of the given system. A newly developed numerical scheme for fractional-order systems introduced by Toufik and Atangana is utilized to obtain the phase portraits of the suggested system for different fractional derivative orders and different parameter values of the system. Analysis on the local stability of the fractional model via the Matignon criteria showed that the trivial equilibrium point is unstable. The dynamics of the system are investigated using Lyapunov exponents for the characterization of the nature of the chaos and to verify the dissipativity of the system. It is shown that the supposed system is chaotic and it is significantly sensitive to parameter variation and small initial condition changes.

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