Effect of random parameter switching on commensurate fractional order chaotic systems. (October 2016)

• Record Type: Journal Article
• Authors: Das, Saptarshi; Pan, Indranil; Das, Shantanu
• Is Part Of: Chaos, solitons and fractals. Volume 91(2016)
• Page Start: 157
• Page End: 173
• Publication Date: 2016-10
• Subjects: Fractional order chaos -- Lorenz-Lu-Chen family -- Lyapunov exponent -- Noise-induced chaos -- Random parameter switched chaos -- Unified chaotic system; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2016.05.014
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: Random switching is studied in fractional order unified chaotic system. The key parameter of unified system is randomly switched at each time instant. Characteristics of the system changes randomly amongst Lorenz, Lu and Chen family. Random parameter switching breaks the chaotic behaviour at lower fractional order. Lyapunov exponent, entropy are used to characterize deterministic/stochastic behaviour. 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.