An Extremely Simple Chaotic System With Infinitely Many Coexisting Attractors

Abstract

The discovery of simple chaotic systems with complex dynamics has always been an interesting research work. This brief aims to construct an extremely simple chaotic system with infinitely many coexisting chaotic attractors. The system consists of five terms with two nonlinearities, and has an infinite number of unstable equilibria owing to its sinusoidal nonlinearity. The most prominent feature of the system is that it coexists infinitely many chaotic attractors for different initial values and fixed system parameters. To our best knowledge, there is no 3-D system with such a simple mathematical model can produce infinitely many coexisting chaotic attractors. The phenomenon of coexisting attractors of the new system is numerically investigated. The circuit and microcontroller-based implementation of the system are presented as well.