Chaos Generation With Impulse Control: Application to Non-Chaotic Systems and Circuit Design
Kun Tian, Celso Grebogi, Hai‐Peng Ren
Abstract
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.