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.

A New Dynamic System Analysis

2013 ◽  
Vol 392 ◽  
pp. 222-226
Author(s):  
Bao Liang Mi ◽  
Guo Zeng Wu
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Dynamic System ◽  
Bifurcation Diagram ◽  
Chaotic System ◽  
System Analysis ◽  
Electronic Circuit ◽  
Circuit Implementation ◽  
Dynamical Properties ◽  
Electronic Circuit Implementation

A new four-dimensional chaotic system is presented in this paper. Some basic dynamical Properties of this chaotic system are investigated by means of Poincaré mapping, Lyapunov exponents and bifurcation diagram. The dynamical behaviours of this system are proved not only by performing numerical simulation and brief theoretical analysis but also by conducting an electronic circuit implementation.

Generating coexisting attractors from a new four-dimensional chaotic system

2020 ◽  
pp. 2150035
Author(s):  
Yan-Mei Hu ◽  
Bang-Cheng Lai
Keyword(s):  
Chaotic System ◽  
Infinite Number ◽  
Linear Functions ◽  
Chaotic Attractors ◽  
Dynamic Evolution ◽  
Coexisting Attractors ◽  
Evolution Analysis ◽  
Fixed Parameter ◽  
Parameter Values ◽  
Multiple Coexisting Attractors

This paper introduces a new four-dimensional chaotic system with a unique unstable equilibrium and multiple coexisting attractors. The dynamic evolution analysis shows that the system concurrently generates two symmetric chaotic attractors for fixed parameter values. Based on this system, an effective method is established to construct an infinite number of coexisting chaotic attractors. It shows that the introduction of some non-linear functions with multiple zeros can increase the equilibria and inspire the generation of coexisting attractor of the system. Numerical simulations verify the availability of the method.

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

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.

Dynamical analysis and passive control of a new 4D chaotic system with multiple attractors

2018 ◽  
Vol 32 (22) ◽  
pp. 1850260 ◽  
Author(s):  
Long Wang ◽  
Mei Ding
Keyword(s):  
Chaotic System ◽  
Passive Control ◽  
Strange Attractors ◽  
Dynamical Analysis ◽  
Bifurcation Diagrams ◽  
Multiple Attractors ◽  
Initial Values ◽  
System A ◽  
Periodic Attractors ◽  
Theoretical Results

This paper constructs a new 4D chaotic system from the Sprott B system. The system is dissipative, chaotic with two saddle foci. The bifurcation diagrams verify that the system exists multiple attractors with different initial values, including two strange attractors, two periodic attractors. Furthermore, we apply the passive control to control the system. A controller is designed for driving the system to the origin. The simulations show our theoretical results visually.

Analysis and Circuit Simulation of New Five Terms Chaotic System

2013 ◽  
Vol 275-277 ◽  
pp. 825-829 ◽  
Author(s):  
Guo Qing Huang
Keyword(s):  
Numerical Simulation ◽  
Power Spectrum ◽  
Differential Equations ◽  
Lyapunov Exponents ◽  
Chaotic System ◽  
Chaotic Attractor ◽  
Electronic Circuit ◽  
Circuit Simulation ◽  
Theory Analysis ◽  
New Chaotic Attractor

A new chaotic attractor is reported with only five terms in three simple differential equations. The system is not only studied via theory analysis and numerical simulation, such as Lyapunov exponents, power spectrum and poincaré section and bifurcations diagrams, but also implemented via an electronic circuit designed by Multisim software

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