Complex dynamics in a 5-D hyper-chaotic attractor with four-wing, one equilibrium and multiple chaotic attractors

Abstract

In this paper, a new five-dimensional autonomous hyper-chaotic attractor with complex dynamics is introduced. Nonlinear behavior of the proposed system is different with most well-known chaotic and hyper-chaotic attractors and exists interesting aspects in this system. There are eight parameters to control with only one equilibrium point, and the new dynamics can generate four-wing hyper-chaotic and chaotic attractors for some specific parameters and initial conditions. One remarkable feature of the new system is that it can generate double-wing and four-wing smooth chaotic attractors with special appearance. By using the symmetry properties about the coordinates, initial conditions and bifurcation diagrams, many schemes are presented to indicate multi-scroll or multi-wing systems. The phenomenon of multiple attractors is discussed, which means that several attractors created simultaneously from different initial values, and according to this phenomenon, many strange attractors are obtained. Detailed information on the dynamic of the new system is obtained numerically by means of phase portraits, sensitivity to initial conditions, Lyapunov exponents spectrum, bifurcation diagrams and Poincare maps. The stability analysis of the new attractors has been investigated to understand dynamical behaviors nearby equilibrium points.