Local bifurcation analysis and ultimate bound of a novel 4D hyper-chaotic system

This paper presents a new four-dimensional smooth quadratic autonomous hyper-chaotic system which can generate novel two double-wing periodic, quasi-periodic and hyper-chaotic attractors. The Lyapunov exponent spectrum, bifurcation diagram and phase portrait are provided. It is shown that this system has a wide hyper-chaotic parameter. The pitchfork bifurcation and Hopf bifurcation are discussed using the center manifold theory. The ellipsoidal ultimate bound of the typical hyper-chaotic attractor is observed. Numerical simulations are given to demonstrate the evolution of the two bifurcations and show the ultimate boundary region.