Analysis and Numerical Simulation of a Novel Four-dimensional Dynamic Evolution System with Multilayer Chaotic Attractors

This paper proposes a novel four-dimensional autonomous system which has complex chaotic dynamics behaviors and gives analysis of novel system. More importantly, the novel system can generate three-layer chaotic attractor, four-layer chaotic attractor, five-layer chaotic attractor, multilayer chaotic attractor by choosing different parameters and initial condition. We analyze the new system by means of phase portraits, Lyapunov exponent spectrum, fractional dimension and bifurcation diagram of the system. The four-dimensional autonomous system is totally different from the well-known systems in previous work. Linear feedback control methods are used to suppress chaos to unstable equilibrium. Numerical simulations are presented to show these results.