scholarly journals Dynamic Analysis and Finite-Time Synchronization of a New Hyperchaotic System With Coexisting Attractors

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 52896-52902 ◽  
Author(s):  
Chengqun Zhou ◽  
Chunhua Yang ◽  
Degang Xu ◽  
Chao-Yang Chen
Keyword(s):  
Dynamic Analysis ◽  
Finite Time ◽  
Time Synchronization ◽  
Hyperchaotic System ◽  
Coexisting Attractors ◽  
New Hyperchaotic System

scholarly journals Finite-Time Adaptive Synchronization of a New Hyperchaotic System with Uncertain Parameters

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Ma Yongguang ◽  
Dong Zijian
Keyword(s):  
Finite Time ◽  
Time Synchronization ◽  
Adaptive Synchronization ◽  
Control Law ◽  
Hyperchaotic System ◽  
Finite Time Stability ◽  
Synchronization Scheme ◽  
New Hyperchaotic System ◽  
Hyperchaotic Systems ◽  
Adaptive Control Law

This paper presents a finite-time adaptive synchronization strategy for a class of new hyperchaotic systems with unknown slave system’s parameters. Based on the finite-time stability theory, an adaptive control law is derived to make the states of the new hyperchaotic systems synchronized in finite-time. Numerical simulations are presented to show the effectiveness of the proposed finite time synchronization scheme.

A Novel Simple Hyperchaotic System with Two Coexisting Attractors

2019 ◽  
Vol 29 (14) ◽  
pp. 1950203 ◽  
Author(s):  
Jiaopeng Yang ◽  
Zhengrong Liu
Keyword(s):  
Complex Dynamics ◽  
Chaotic Dynamic ◽  
Cross Product ◽  
Hyperchaotic System ◽  
Compound Structure ◽  
Coexisting Attractors ◽  
Dynamical Behaviors ◽  
Periodic Attractors ◽  
New Hyperchaotic System ◽  
New System

This article introduces a new hyperchaotic system of four-dimensional autonomous ordinary differential equations, with only cubic cross-product nonlinearities, which can respectively display two hyperchaotic attractors with only nonhyperbolic equilibria line. Several issues such as basic dynamical behaviors, routes to chaos, bifurcations, periodic windows, and the compound structure of the new hyperchaotic and chaotic system are investigated, either theoretically or numerically. Of particular interest is the fact that the two coexisting attractors of the new hyperchaotic system are symmetrical, and this hyperchaotic system can generate plenty of complex dynamics including two coexisting chaotic or periodic attractors. Moreover, some chaotic features of the attractor are justified numerically. Finally, 0-1 test is used to analyze and describe the complex chaotic dynamic behavior of the new system.

scholarly journals Finite-Time Synchronization of Chaotic Systems with Different Dimension and Secure Communication

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Shouquan Pang ◽  
Yu Feng ◽  
Yongjian Liu
Keyword(s):  
Finite Time ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Time Synchronization ◽  
Secure Communications ◽  
Hyperchaotic System ◽  
Uncertain Parameters ◽  
Three Dimension ◽  
Electronic Circuits ◽  
Lorenz Chaotic System

Finite-time synchronization of chaotic systems with different dimension and secure communication is investigated. It is rigorously proven that global finite-time synchronization can be achieved between three-dimension Lorenz chaotic system and four-dimension Lorenz hyperchaotic system which have certain parameters or uncertain parameters. The electronic circuits of finite-time synchronization using Multisim 12 are designed to verify our conclusion. And the application to the secure communications is also analyzed and discussed.

scholarly journals Hidden Coexisting Attractors in a Fractional-Order System without Equilibrium: Analysis, Circuit Implementation, and Finite-Time Synchronization

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Guangchao Zheng ◽  
Ling Liu ◽  
Chongxin Liu
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Finite Time ◽  
Secure Communication ◽  
Time Synchronization ◽  
Basins Of Attraction ◽  
Fractional Order System ◽  
Equilibrium Analysis ◽  
Order System ◽  
Coexisting Attractors

In this paper, a novel three-dimensional fractional-order chaotic system without equilibrium, which can present symmetric hidden coexisting chaotic attractors, is proposed. Dynamical characteristics of the fractional-order system are analyzed fully through numerical simulations, mainly including finite-time local Lyapunov exponents, bifurcation diagram, and the basins of attraction. In particular, the system can generate diverse coexisting attractors varying with different orders, which presents ample and complex dynamic characteristics. And there is great potential for secure communication. Then electronic circuit of the fractional-order system is designed to help verify its effectiveness. What is more, taking the disturbances into account, a finite-time synchronization of the fractional-order chaotic system without equilibrium is achieved and the improved controller is proven strictly by applying finite-time stable theorem. Eventually, simulation results verify the validity and rapidness of the proposed method. Therefore, the fractional-order chaotic system with hidden attractors can present better performance for practical applications, such as secure communication and image encryption, which deserve further investigation.

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