A 4-D chaos with fully qualified four-wing type

Abstract

In this paper we propose a new simple four-dimensional (4D) chaotic system by introducing a nonlinear state feedback controller. There is a fully qualified four-wing type in all directions of the chaotic attractor. With a larger positive Lyapunov exponent, some interesting and complex dynamic behaviors are obtained. Basic dynamical properties of the four-wing attractor are studied by numerical and theoretical analyses, such as dissipativity equilibria, Poincaré map, spectrum map, continuous spectrum and chaotic behaviors. The sensitivities of system parameters to the chaotic behaviors are further explored by calculating, in detail, its Lyapunov exponent spectrum and bifurcation diagrams. Finally, an oscillator circuit is designed for implementation. The EWB observation results are in reasonable agreement with the numerical simulation results.