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.

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.

Dynamical analysis of a new multistable chaotic system with hidden attractor: Antimonotonicity, coexisting multiple attractors, and offset boosting

2019 ◽  
Vol 383 (13) ◽  
pp. 1450-1456 ◽  
Author(s):  
Atiyeh Bayani ◽  
Karthikeyan Rajagopal ◽  
Abdul Jalil M. Khalaf ◽  
Sajad Jafari ◽  
G.D. Leutcho ◽  
...  
Keyword(s):  
Chaotic System ◽  
Dynamical Analysis ◽  
Hidden Attractor ◽  
Multiple Attractors ◽  
Offset Boosting

Generating Four-Wing Hyperchaotic Attractor and Two-Wing, Three-Wing, and Four-Wing Chaotic Attractors in 4D Memristive System

2017 ◽  
Vol 27 (02) ◽  
pp. 1750027 ◽  
Author(s):  
Ling Zhou ◽  
Chunhua Wang ◽  
Lili Zhou
Keyword(s):  
Chaotic System ◽  
Three Dimensional ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Hyperchaotic System ◽  
Multiple Attractors ◽  
System A ◽  
Dynamical Behaviors ◽  
Memristive System ◽  
Line Of Equilibria

By adding only one smooth flux-controlled memristor into a three-dimensional (3D) pseudo four-wing chaotic system, a new real four-wing hyperchaotic system is constructed in this paper. It is interesting to see that this new memristive chaotic system can generate a four-wing hyperchaotic attractor with a line of equilibria. Moreover, it can generate two-, three- and four-wing chaotic attractors with the variation of a single parameter which denotes the strength of the memristor. At the same time, various coexisting multiple attractors (e.g. three-wing attractors, four-wing attractors and attractors with state transition under the same system parameters) are observed in this system, which means that extreme multistability arises. The complex dynamical behaviors of the proposed system are analyzed by Lyapunov exponents (LEs), phase portraits, Poincaré maps, and time series. An electronic circuit is finally designed to implement the hyperchaotic memristive system.

scholarly journals A New Chaotic System with Only Nonhyperbolic Equilibrium Points: Dynamics and Its Engineering Application

Complexity ◽  
2022 ◽  
Vol 2022 ◽  
pp. 1-16
Author(s):  
Maryam Zolfaghari-Nejad ◽  
Mostafa Charmi ◽  
Hossein Hassanpoor
Keyword(s):  
Chaotic System ◽  
Infinite Number ◽  
Equilibrium Points ◽  
Engineering Application ◽  
Period Doubling ◽  
Spectral Entropy ◽  
Multiple Attractors ◽  
Initial Values ◽  
New Chaotic System ◽  
New System

In this work, we introduce a new non-Shilnikov chaotic system with an infinite number of nonhyperbolic equilibrium points. The proposed system does not have any linear term, and it is worth noting that the new system has one equilibrium point with triple zero eigenvalues at the origin. Also, the novel system has an infinite number of equilibrium points with double zero eigenvalues that are located on the z -axis. Numerical analysis of the system reveals many strong dynamics. The new system exhibits multistability and antimonotonicity. Multistability implies the coexistence of many periodic, limit cycle, and chaotic attractors under different initial values. Also, bifurcation analysis of the system shows interesting phenomena such as periodic window, period-doubling route to chaos, and inverse period-doubling bifurcations. Moreover, the complexity of the system is analyzed by computing spectral entropy. The spectral entropy distribution under different initial values is very scattered and shows that the new system has numerous multiple attractors. Finally, chaos-based encoding/decoding algorithms for secure data transmission are developed by designing a state chain diagram, which indicates the applicability of the new chaotic system.

scholarly journals Abundant Coexisting Multiple Attractors’ Behaviors in Three-Dimensional Sine Chaotic System

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Huagan Wu ◽  
Han Bao ◽  
Quan Xu ◽  
Mo Chen
Keyword(s):  
Chaotic System ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
Multiple Attractors ◽  
One Dimensional ◽  
System Parameters ◽  
Initial Values ◽  
Power Simulation ◽  
Attraction Basins ◽  
Index 2

This paper presents a novel and simple three-dimensional (3-D) chaotic system by introducing two sine nonlinearities into a simple 3-D linear dynamical system. The presented sine system possesses nine equilibrium points consisting of five index-2 saddle foci and four index-1 saddle foci which allow the coexistence of various types of disconnected attractors, also known as multistability. The coexisting multiple attractors are depicted by the phase plots and attraction basins. Coexisting bifurcation modes triggered by different initial values are numerically simulated by two-dimensional bifurcation and complexity plots under two sets of initial values and one-dimensional bifurcation plots under three sets of initial values, which demonstrate that the abundant coexisting multiple attractors’ behaviors in the presented sine system are related not only to the system parameters but also to the initial values. A simulation-oriented circuit model is synthesized, and PSIM (power simulation) screen captures well validate the numerical simulations.

Passive control of chaotic system with multiple strange attractors

2006 ◽  
Vol 15 (10) ◽  
pp. 2266-2270 ◽  
Author(s):  
Song Yun-Zhong ◽  
Zhao Guang-Zhou ◽  
Qi Dong-Lian
Keyword(s):  
Chaotic System ◽  
Passive Control ◽  
Strange Attractors

scholarly journals Dynamical Analysis of a Novel 4-D Hyper-Chaotic System With One Non-Hyperbolic Equilibrium Point and Application in Secure Communication

2020 ◽  
Vol 9 (4) ◽  
pp. 74-99
Author(s):  
Pushali Trikha ◽  
Lone Seth Jahanzaib
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Equilibrium Points ◽  
Dynamical Analysis ◽  
The Novel ◽  
Bifurcation Diagrams ◽  
Dynamical Properties ◽  
Hyperbolic Equilibrium ◽  
Hyperbolic Equilibrium Point

In this article, a novel hyper-chaotic system has been introduced and its dynamical properties (i.e., phase plots, time series, lyapunov exponents, bifurcation diagrams, equilibrium points, Poincare sections, etc.) have been studied. Also, the novel chaotic systems have been synchronized using novel synchronization technique multi-switching compound difference synchronization and its application have been shown in the field of secure communication. Numerical simulations have been undertaken to validate the efficacy of the synchronization in secure communication.

scholarly journals Heterogeneous and Homogenous Multistabilities in a Novel 4D Memristor-Based Chaotic System with Discrete Bifurcation Diagrams

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Lilian Huang ◽  
Wenju Yao ◽  
Jianhong Xiang ◽  
Zefeng Zhang
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Large Range ◽  
Circuit Simulation ◽  
Chaotic Attractors ◽  
Bifurcation Diagrams ◽  
Coexisting Attractors ◽  
Initial Values ◽  
The Relationship ◽  
New System

In this paper, a new 4D memristor-based chaotic system is constructed by using a smooth flux-controlled memristor to replace a resistor in the realization circuit of a 3D chaotic system. Compared with general chaotic systems, the chaotic system can generate coexisting infinitely many attractors. The proposed chaotic system not only possesses heterogeneous multistability but also possesses homogenous multistability. When the parameters of system are fixed, the chaotic system only generates two kinds of chaotic attractors with different positions in a very large range of initial values. Different from other chaotic systems with continuous bifurcation diagrams, this system has discrete bifurcation diagrams when the initial values change. In addition, this paper reveals the relationship between the symmetry of coexisting attractors and the symmetry of initial values in the system. The dynamic behaviors of the new system are analyzed by equilibrium point and stability, bifurcation diagrams, Lyapunov exponents, and phase orbit diagrams. Finally, the chaotic attractors are captured through circuit simulation, which verifies numerical simulation.

A new hyperchaotic system from T chaotic system: dynamical analysis, circuit implementation, control and synchronization

Circuit World ◽  
2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Selcuk Emiroglu ◽  
Akif Akgül ◽  
Yusuf Adıyaman ◽  
Talha Enes Gümüş ◽  
Yılmaz Uyaroglu ◽  
...  
Keyword(s):  
Chaotic System ◽  
Passive Control ◽  
Control Method ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Dynamical Analysis ◽  
Hyperchaotic System ◽  
Content Type ◽  
Control And Synchronization ◽  
New Hyperchaotic System

Purpose The purpose of this paper is to develop new four-dimensional (4D) hyperchaotic system by adding another state variable and linear controller to three-dimensional T chaotic dynamical systems. Its dynamical analyses, circuit experiment, control and synchronization applications are presented. Design/methodology/approach A new 4D hyperchaotic attractor is achieved through a simulation, circuit experiment and mathematical analysis by obtaining the Lyapunov exponent spectrum, equilibrium, bifurcation, Poincaré maps and power spectrum. Moreover, hardware experimental measurements are performed and obtained results well validate the numerical simulations. Also, the passive control method is presented to make the new 4D hyperchaotic system stable at the zero equilibrium and synchronize the two identical new 4D hyperchaotic system with different initial conditions. Findings The passive controllers can stabilize the new 4D chaotic system around equilibrium point and provide the synchronization of new 4D chaotic systems with different initial conditions. The findings from Matlab simulations, circuit design simulations in computer and physical circuit experiment are consistent with each other in terms of comparison. Originality/value The 4D hyperchaotic system is presented, and dynamical analysis and numerical simulation of the new hyperchaotic system were firstly carried out. The circuit of new 4D hyperchaotic system is realized, and control and synchronization applications are performed.

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