Compound Chaotic Systems with Composite Attractors

Abstract

Chaotic systems with either a self-excited attractor or a hidden attractor are prevalent in the research paradigm. But a composite attractor of a chaotic system that exhibits both self-excited attractors and hidden attractors with time is rare. Compounding of a chaotic system is devised to enhance the richness of the system as it exhibits different behaviors with time. This paper presents a two-stage technique for generating a compound-chaotic system by combining eight subsystems from Chameleon chaotic system. The first stage is the design of a nonautonomous piecewise function. The second stage is to generate a compound system using the designed function. The compound system exhibits a composite attractor that is a mix of self-excited and hidden attractors with time. The composite attractor is generated with the variation of the equilibrium points in the eight subsystems due to the designed function. The resultant attractor of the compound-chaotic system is termed as a composite attractor since it has both the self-excited and hidden attractors. Transient chaos and coexistence of attractors are also observed in the system. The proposed compound-chaotic system is analyzed using the available tools and the paper’s claims are validated.