Chaos Generation With Impulse Control: Application to Non-Chaotic Systems and Circuit Design

Chaos has been successfully applied in many fields to improve the performance of engineering systems, such as communication, vibration compact, and mixing. Generating chaos from originally non-chaotic systems is a relevant topic because of potential applications. In this work, the impulse control is...

Full description

Saved in:
Bibliographic Details
Published inIEEE transactions on circuits and systems. I, Regular papers Vol. 68; no. 7; pp. 3012 - 3022
Main Authors Tian, Kun, Grebogi, Celso, Ren, Hai-Peng
Format Journal Article
LanguageEnglish
Published New York IEEE 01.07.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Bifurcation
Chaos
Chaos generation
Chaos theory
Chaotic communication
Chen circuit
Circuit design
Control systems
Delay effects
impulse control
Liapunov exponents
nonlinear dynamics
Numerical methods
Poincare maps
State feedback
topological horseshoe
Trajectory
Online AccessGet full text

Cover

More Information
Summary:Chaos has been successfully applied in many fields to improve the performance of engineering systems, such as communication, vibration compact, and mixing. Generating chaos from originally non-chaotic systems is a relevant topic because of potential applications. In this work, the impulse control is shown to generate chaos from non-chaotic system. Using non-chaotic Chen system as an example, we prove by analytical and numerical methods that chaos is indeed generated. The features of the chaos generated by impulse control are analysed using Lyapunov exponents, bifurcation diagram, power spectrum, Poincaré mapping and Kaplan-Yorke dimension. Furthermore, we demonstrate the chaotic attractor generation by impulse control using a circuit experiment. The last but not minor point is that the existence of topological horseshoe is given by rigorous computer-aided proof.
ISSN:1549-8328
1558-0806
DOI:10.1109/TCSI.2021.3075550