Effect of Random Parameter Switching on Commensurate Fractional Order Chaotic Systems

TL;DR

This study investigates how random parameter switching in fractional order chaotic systems can suppress chaos, using simulations and various analysis methods, potentially aiding in chaos control in practical applications.

Contribution

It introduces the effect of random parameter switching on commensurate fractional order chaotic systems and demonstrates chaos suppression through simulation analysis.

Findings

Random parameter switching suppresses chaos earlier than fixed parameters.

Lyapunov exponent and Shannon entropy characterize chaos suppression.

Different simulation techniques influence the analysis of switched chaotic systems.

Abstract

The paper explores the effect of random parameter switching in a fractional order (FO) unified chaotic system which captures the dynamics of three popular sub-classes of chaotic systems i.e. Lorenz, Lu and Chen's family of attractors. The disappearance of chaos in such systems which rapidly switch from one family to the other has been investigated here for the commensurate FO scenario. Our simulation study show that a noise-like random variation in the key parameter of the unified chaotic system along with a gradual decrease in the commensurate FO is capable of suppressing the chaotic fluctuations much earlier than that with the fixed parameter one. The chaotic time series produced by such random parameter switching in nonlinear dynamical systems have been characterized using the largest Lyapunov exponent (LLE) and Shannon entropy. The effect of choosing different simulation techniques for random parameter FO switched chaotic systems have also been explored through two frequency domain and three time domain methods. Such a noise-like random switching mechanism could be useful for stabilization and control of chaotic oscillation in many real-world applications.