Dynamical analysis and electronic circuit realization of an equilibrium free 3D chaotic system with a large number of coexisting attractors

Optik ◽  
2017 ◽  
Vol 130 ◽  
pp. 356-364 ◽  
Author(s):  
Z.T. Njitacke ◽  
J. Kengne ◽  
A. Nguomkam Negou
Keyword(s):  
Chaotic System ◽  
Electronic Circuit ◽  
Dynamical Analysis ◽  
Coexisting Attractors ◽  
Circuit Realization

Various Types of Coexisting Attractors in a New 4D Autonomous Chaotic System

2017 ◽  
Vol 27 (09) ◽  
pp. 1750142 ◽  
Author(s):  
Qiang Lai ◽  
Akif Akgul ◽  
Xiao-Wen Zhao ◽  
Huiqin Pei
Keyword(s):  
Numerical Simulation ◽  
Dynamic Behavior ◽  
Chaotic System ◽  
Limit Cycles ◽  
Electronic Circuit ◽  
Strange Attractors ◽  
Bifurcation Diagrams ◽  
Coexisting Attractors ◽  
Signum Function ◽  
Multiple Coexisting Attractors

An unique 4D autonomous chaotic system with signum function term is proposed in this paper. The system has four unstable equilibria and various types of coexisting attractors appear. Four-wing and four-scroll strange attractors are observed in the system and they will be broken into two coexisting butterfly attractors and two coexisting double-scroll attractors with the variation of the parameters. Numerical simulation shows that the system has various types of multiple coexisting attractors including two butterfly attractors with four limit cycles, two double-scroll attractors with a limit cycle, four single-scroll strange attractors, four limit cycles with regard to different parameters and initial values. The coexistence of the attractors is determined by the bifurcation diagrams. The chaotic and hyperchaotic properties of the attractors are verified by the Lyapunov exponents. Moreover, we present an electronic circuit to experimentally realize the dynamic behavior of the system.

scholarly journals Dynamical analysis and FPGA implementation of a large range chaotic system with coexisting attractors

2018 ◽  
Vol 11 ◽  
pp. 368-376 ◽  
Author(s):  
Yong-ju Xian ◽  
Cheng Xia ◽  
Tao-tao Guo ◽  
Kun-rong Fu ◽  
Chang-biao Xu
Keyword(s):  
Chaotic System ◽  
Large Range ◽  
Fpga Implementation ◽  
Dynamical Analysis ◽  
Coexisting Attractors

A new three-dimensional chaotic system, its dynamical analysis and electronic circuit applications

Optik ◽  
2016 ◽  
Vol 127 (18) ◽  
pp. 7062-7071 ◽  
Author(s):  
Akif Akgul ◽  
Shafqat Hussain ◽  
Ihsan Pehlivan
Keyword(s):  
Chaotic System ◽  
Electronic Circuit ◽  
Three Dimensional ◽  
Dynamical Analysis

scholarly journals A New Double-Wing Chaotic System With Coexisting Attractors and Line Equilibrium: Bifurcation Analysis and Electronic Circuit Simulation

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 115454-115462 ◽  
Author(s):  
Aceng Sambas ◽  
Sundarapandian Vaidyanathan ◽  
Sen Zhang ◽  
Yicheng Zeng ◽  
Mohamad Afendee Mohamed ◽  
...  
Keyword(s):  
Chaotic System ◽  
Bifurcation Analysis ◽  
Electronic Circuit ◽  
Circuit Simulation ◽  
Coexisting Attractors ◽  
Electronic Circuit Simulation ◽  
Line Equilibrium

Dynamical analysis, FPGA implementation and synchronization for secure communication of new chaotic system with hidden and coexisting attractors

2021 ◽  
Author(s):  
Qiang Lai ◽  
Ziling Wang ◽  
Paul Didier Kamdem Kuate
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Analog Circuit ◽  
Control Method ◽  
Simulation Analysis ◽  
Period Doubling ◽  
Fpga Implementation ◽  
Dynamical Analysis ◽  
Hidden Attractors ◽  
Coexisting Attractors

This paper proposes an interesting autonomous chaotic system with hidden attractors and coexisting attractors. The system has no equilibrium, one equilibrium, three equilibria and line equilibria for different parameter regions. The existence of hidden attractors and coexisting attractors of the system has been revealed by using simulation analysis. The bifurcation diagram shows the period-doubling bifurcation route to chaos with the variation of parameters. The analog circuit and FPGA implementation of the system are presented. The synchronization for secure communication of the system is investigated. The synchronization conditions are established by using the adaptive control method.

scholarly journals A New 4-D Chaotic System with Hidden Attractor and its Circuit Implementation

2018 ◽  
Vol 7 (3) ◽  
pp. 1245 ◽  
Author(s):  
Aceng Sambas ◽  
Mustafa Mamat ◽  
Sundarapandian Vaidyanathan ◽  
Muhammad Mohamed ◽  
Mada Sanjaya
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Chaotic Behavior ◽  
Phase Portraits ◽  
Hidden Attractor ◽  
Circuit Realization ◽  
New Chaotic System ◽  
Quadratic Nonlinearities ◽  
Work First

In the chaos literature, there is currently significant interest in the discovery of new chaotic systems with hidden chaotic attractors. A new 4-D chaotic system with only two quadratic nonlinearities is investigated in this work. First, we derive a no-equilibrium chaotic system and show that the new chaotic system exhibits hidden attractor. Properties of the new chaotic system are analyzed by means of phase portraits, Lyapunov chaos exponents, and Kaplan-Yorke dimension. Then an electronic circuit realization is shown to validate the chaotic behavior of the new 4-D chaotic system. Finally, the physical circuit experimental results of the 4-D chaotic system show agreement with numerical simulations.

scholarly journals Dynamical Analysis and Periodic Solution of a Chaotic System with Coexisting Attractors

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Mingshu Chen ◽  
Zhen Wang ◽  
Xiaojuan Zhang ◽  
Huaigu Tian
Keyword(s):  
Chaotic System ◽  
Vector Fields ◽  
Dynamical Analysis ◽  
Stable Node ◽  
Polynomial Vector Fields ◽  
Coexisting Attractors ◽  
Poincaré Compactification ◽  
Unstable Node ◽  
New Chaotic System ◽  
Multiple Coexisting Attractors

Chaotic attractors with no equilibria, with an unstable node, and with stable node-focus are presented in this paper. The conservative solutions are investigated by the semianalytical and seminumerical method. Furthermore, multiple coexisting attractors are investigated, and circuit is carried out. To study the system’s global structure, dynamics at infinity for this new chaotic system are studied using Poincaré compactification of polynomial vector fields in R 3 . Meanwhile, the dynamics near the infinity of the singularities are obtained by reducing the system’s dimensions on a Poincaré ball. The averaging theory analyzes the periodic solution’s stability or instability that bifurcates from Hopf-zero bifurcation.

Symmetric coexisting attractors and extreme multistability in chaotic system

2021 ◽  
pp. 2150458
Author(s):  
Xiaoxia Li ◽  
Chi Zheng ◽  
Xue Wang ◽  
Yingzi Cao ◽  
Guizhi Xu
Keyword(s):  
Chaotic System ◽  
Electronic Circuit ◽  
Phase Portraits ◽  
Hyperchaotic System ◽  
Coexisting Attractors ◽  
Extreme Multistability ◽  
New Chaotic System ◽  
Initial States ◽  
Parameter Ranges ◽  
New System

In this paper, a new four-dimensional (4D) chaotic system with two cubic nonlinear terms is proposed. The most striking feature is that the new system can exhibit completely symmetric coexisting bifurcation behaviors and four symmetric coexisting attractors with the same Lyapunov exponents in all parameter ranges of the system when taking different initial states. Interestingly, these symmetric coexisting attractors can be considered as unusual symmetrical rotational coexisting attractors, which is a very fascinating phenomenon. Furthermore, by using a memristor to replace the coupling resistor of the new system, an interesting 4D memristive hyperchaotic system with one unstable origin is constructed. Of particular surprise is that it can exhibit four groups of extreme multistability phenomenon of infinitely many coexisting attractors of symmetric distribution about the origin. By using phase portraits, Lyapunov exponent spectra, and coexisting bifurcation diagrams, the dynamics of the two systems are fully analyzed and investigated. Finally, the electronic circuit model of the new system is designed for verifying the feasibility of the new chaotic system.

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