Coexisting attractors and circuit implementation of a new 4D chaotic system with two equilibria

2018 ◽  
Vol 107 ◽  
pp. 92-102 ◽  
Author(s):  
Qiang Lai ◽  
Tsafack Nestor ◽  
Jacques Kengne ◽  
Xiao-Wen Zhao
Keyword(s):  
Chaotic System ◽  
Circuit Implementation ◽  
Coexisting Attractors ◽  
Two Equilibria

scholarly journals Composite One- to Six-Scroll Hidden Attractors in a Memristor-Based Chaotic System and Their Circuit Implementation

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Ying Li ◽  
Xiaozhu Xia ◽  
Yicheng Zeng ◽  
Qinghui Hong
Keyword(s):  
Fixed Point ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Circuit Implementation ◽  
Hidden Attractors ◽  
Coexisting Attractors ◽  
Extreme Multistability ◽  
Different Types ◽  
Hardware Circuit ◽  
New System

Chaotic systems with hidden multiscroll attractors have received much attention in recent years. However, most parts of hidden multiscroll attractors previously reported were repeated by the same type of attractor, and the composite of different types of attractors appeared rarely. In this paper, a memristor-based chaotic system, which can generate composite attractors with one up to six scrolls, is proposed. These composite attractors have different forms, similar to the Chua’s double scroll and jerk double scroll. Through theoretical analysis, we find that the new system has no fixed point; that is to say, all of the composite multiscroll attractors are hidden attractors. Additionally, some complicated dynamic behaviors including various hidden coexisting attractors, extreme multistability, and transient transition are explored. Moreover, hardware circuit using discrete components is implemented, and its experimental results supported the numerical simulations results.

Coexisting attractors, circuit realization and impulsive synchronization of a new four-dimensional chaotic system

2019 ◽  
Vol 33 (03) ◽  
pp. 1950026 ◽  
Author(s):  
Chengqun Zhou ◽  
Chunhua Yang ◽  
Degang Xu ◽  
Chaoyang Chen
Keyword(s):  
Chaotic System ◽  
Control Method ◽  
Impulsive Control ◽  
Period Doubling ◽  
Coexisting Attractors ◽  
Circuit Realization ◽  
Impulsive Synchronization ◽  
Periodic Attractors ◽  
Different Types ◽  
Two Equilibria

This paper presents a new four-dimensional chaotic system with three nonlinearities and two equilibria. The most striking feature of the new system is that it has different types of asymmetric coexisting attractors. Simulation experiments are used to study the complex dynamic behaviors of the system. The chaos, period-doubling bifurcation, coexisting attractors with respect to system parameters and initial values are found in the system. It shows that the system has coexisting chaotic attractors, coexisting periodic attractors, coexisting chaotic and periodic attractors. The electronic circuit is applied to implement the chaotic attractor and coexisting attractors for studying the physical significance of the system. In addition, we consider the synchronization of the system by using the impulsive control method. Some synchronization criteria are established via theoretical analysis and simulation example.

scholarly journals Coexisting Attractors and Multistability in a Simple Memristive Wien-Bridge Chaotic Circuit

Entropy ◽  
2019 ◽  
Vol 21 (7) ◽  
pp. 678 ◽  
Author(s):  
Yixuan Song ◽  
Fang Yuan ◽  
Yuxia Li
Keyword(s):  
Chaotic System ◽  
Analog Circuit ◽  
Random Sequence ◽  
Mathematical Expression ◽  
Digital Signal ◽  
Approximate Entropy ◽  
Chaotic Circuit ◽  
Coexisting Attractors ◽  
Key Space ◽  
Sequence Generator

In this paper, a new voltage-controlled memristor is presented. The mathematical expression of this memristor has an absolute value term, so it is called an absolute voltage-controlled memristor. The proposed memristor is locally active, which is proved by its DC V–I (Voltage–Current) plot. A simple three-order Wien-bridge chaotic circuit without inductor is constructed on the basis of the presented memristor. The dynamical behaviors of the simple chaotic system are analyzed in this paper. The main properties of this system are coexisting attractors and multistability. Furthermore, an analog circuit of this chaotic system is realized by the Multisim software. The multistability of the proposed system can enlarge the key space in encryption, which makes the encryption effect better. Therefore, the proposed chaotic system can be used as a pseudo-random sequence generator to provide key sequences for digital encryption systems. Thus, the chaotic system is discretized and implemented by Digital Signal Processing (DSP) technology. The National Institute of Standards and Technology (NIST) test and Approximate Entropy analysis of the proposed chaotic system are conducted in this paper.

A Unified Chaotic System with Various Coexisting Attractors

2021 ◽  
Vol 31 (01) ◽  
pp. 2150013
Author(s):  
Qiang Lai
Keyword(s):  
Chaotic System ◽  
Equilibrium Points ◽  
Sine Function ◽  
Coexisting Attractors ◽  
Dynamic Behaviors ◽  
Multiple Zeros ◽  
Unified Chaotic System

This article presents a unified four-dimensional autonomous chaotic system with various coexisting attractors. The dynamic behaviors of the system are determined by its special nonlinearities with multiple zeros. Two cases of nonlinearities with sine function of the system are discussed. The symmetrical coexisting attractors, asymmetrical coexisting attractors and infinitely many coexisting attractors in the system are numerically demonstrated. This shows that such a system has an ability to produce abundant coexisting attractors, depending on the number of equilibrium points determined by nonlinearities.

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 Memristor-Based Scroll Chaotic System — Design, Analysis and Circuit Implementation

2014 ◽  
Vol 24 (07) ◽  
pp. 1450099 ◽  
Author(s):  
Huifang Li ◽  
Lidan Wang ◽  
Shukai Duan
Keyword(s):  
System Design ◽  
Chaotic System ◽  
Dynamic Range ◽  
Mathematical Structure ◽  
Maximum Lyapunov Exponent ◽  
Potential Candidate ◽  
Circuit Implementation ◽  
Memory Element ◽  
Triangular Wave ◽  
Analysis Computer

A scroll chaotic system containing a HP memristor model and triangular wave sequence is proposed in this article. Because the memristor is both a nonlinear element and a memory element intrinsically, it is considered a potential candidate to reduce system power consumption and circuit size. A reasonable mathematical structure of triangular wave sequence and the selection of appropriate amplitude, balance point and turning point reduce the dynamic range of signal input caused by the integrator. The proposed system produces a wealth of chaos, just by changing one parameter. Circuit simulations are conducted and the chaotic attractors can be observed. Theoretical analysis, computer simulation and calculation of maximum Lyapunov exponent have been used to research the basic dynamics of this system. The consistency of circuit implementation and computer simulations verifies the effectiveness of the system design.

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