Generating Planar Multi-Scroll Attractors from a 3D Chaotic System via Switching Control

A three-dimensional quadratic polynomial chaotic system with no constant term is investigated in this paper. The system is described as a differential equation which is composed of five linear terms and three nonlinear terms. A simple single-scroll attractor is generated from the chaotic system with two equilibria. By introducing appropriate sign functions with a series of parameters into a state variable, the system can generate odd or even multi-scroll attractors along a single direction via switching control. Other appropriate sign functions are also introduced into another state variable synchronously. The system can generate planar multi-scroll attractors along two directions. Numerical simulations on multi-scroll attractors are employed to verify the feasibility and effectiveness of the designed sign functions.