Constructing Chaotic Systems from a Class of Switching Systems

2018 ◽  
Vol 28 (02) ◽  
pp. 1850032 ◽  
Author(s):  
Yuping Zhang ◽  
Xinzhi Liu ◽  
Huaiyue Zhang ◽  
Chunhua Jia
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Continuous Time ◽  
Chaotic Systems ◽  
Switching Systems ◽  
Heteroclinic Loop ◽  
Time Switching ◽  
Loop Design ◽  
Implementation Scheme ◽  
Shilnikov Criterion

This paper aims to develop an approach for constructing chaotic systems from a class of linear continuous-time switching systems. First, the Shilnikov criterion is analyzed and extended to the switching systems. Then some kinds of “swing planes” are provided via a heteroclinic loop design, which act as switching planes to chaotify the systems. Furthermore, a numerical example is presented to validate the proposed principle and implementation scheme. The theoretical analysis and numerical simulation have demonstrated the feasibility and effectiveness of the developed techniques.

scholarly journals The Exponential Stabilization of a Class of n-D Chaotic Systems via the Exact Solution Method

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Runzi Luo ◽  
Jiaojiao Fu ◽  
Haipeng Su
Keyword(s):  
Numerical Simulation ◽  
Exact Solution ◽  
Theoretical Analysis ◽  
Chaotic System ◽  
Unknown Parameter ◽  
Chaotic Systems ◽  
Solution Method ◽  
Exponential Stabilization ◽  
Control Approach

This paper treats the exponential stabilization of a class of n-D chaotic systems. A new control approach which is called the exact solution method is presented. The most important feature of this method is that the solution of the system under consideration can be carefully designed to converge exponentially to the origin. Based on this method, the exponential stabilization of a class of n-D chaotic systems and its application in controlling chaotic system with unknown parameter are presented. The Genesio-Tesi system is taken to give the numerical simulation which is completely consistent with the theoretical analysis presented in this paper.

Chaotification of a Class of Linear Switching Systems by Hybrid Driven Methods

2014 ◽  
Vol 24 (03) ◽  
pp. 1450033 ◽  
Author(s):  
Yuping Zhang ◽  
Xinzhi Liu ◽  
Hong Zhu ◽  
Yong Zeng
Keyword(s):  
Lyapunov Exponents ◽  
Continuous Time ◽  
Autonomous Systems ◽  
Phase Portraits ◽  
Computational Formula ◽  
Switching Systems ◽  
Time Switching ◽  
Switching Rule ◽  
Lyapunov Spectra ◽  
Linear Switching Systems

This paper investigates a class of linear continuous-time switching systems and proposes a new approach to generate chaos by designing a hybrid switching rule. First, a computational formula for Lyapunov exponents is derived by extending the definition of Lyapunov exponent for continuous-time autonomous systems to that of a class of linear continuous-time switching systems. Then, a novel switching rule is proposed to gain global boundedness property as well as the required placement of Lyapunov exponents for chaos. A numerical example is given to illustrate the chaotic dynamic behavior of the generated system. The Lyapunov dimension of the system in the example is calculated and the corresponding bifurcation diagram and Lyapunov spectra are sketched, which, together with other phase portraits, clearly verify the validity of the main result.

scholarly journals Controlling Chaotic Systems via Time-delayed Control

2021 ◽  
Vol 15 ◽  
pp. 44-49
Author(s):  
Ramy Farid ◽  
Abdul-Azim Ibrahim ◽  
Belal Abou-Zalam
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Chaotic Systems ◽  
Equilibrium Points ◽  
Unstable Equilibrium ◽  
Chaotic Attractors ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Integral Time ◽  
Lyapunov Stabilization

Based on Lyapunov stabilization theory, this paper proposes a proportional plus integral time-delayed controller to stabilize unstable equilibrium points (UPOs) embedded in chaotic attractors. The criterion is successfully applied to the classic Chua's circuit. Theoretical analysis and numerical simulation show the effectiveness of this controller.

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