An Extremely Multistable Complex Chaotic System Under Boosting Control

Abstract

In order to explore the phenomenon of coexisting attractors in complex chaotic systems, a multistable complex chaotic system is designed by using a cosine function and a control parameter to control the Sprott B system in this paper. The basic features of the complex chaotic system are analyzed from the perspectives of symmetry, dissipation, equilibrium points and stability. The analysis results indicate that the complex chaotic system is a symmetrical and dissipative system. It is particularly interesting to note that the system has infinitely many unstable equilibrium points, which generate infinitely many attractors. The dynamical characteristics of the complex chaotic system are evaluated through bifurcation diagrams, spectral entropy complexity and Lyapunov exponents spectrum. The dynamical evaluations illustrate that the system has complex dynamical performances, such as chaotic states, periodic states, especially infinitely many coexisting attractors. Then a chaotic circuit based on the complex chaotic system is designed and simulated by Multisim software. And the hardware circuit is implemented by using digital signal processor (DSP) platform. The hardware experimental results are consistent with the Multisim simulation results.