Simplified hyper-chaotic systems generating multi-wing non-equilibrium attractors

Abstract

Abstract By a simple feedback control, a new hyper-chaotic system was constructed based on a three-dimensional Lorenz-like chaotic system. This hyper-chaotic system can show butterfly shape (two-wing) strange attractor. The remarkable feature of this system is that it has no equilibrium. By Lyapunov exponents, bifurcation diagram and Poincare maps, the dynamical behaviors of the proposed system were analyzed; and this system was also realized by an electronic circuit. To extend this two-wing non-equilibrium hyper-chaotic system to multi-wing chaotic systems, a piecewise-linear (PWL) function was designed and applied to the proposed hyper-chaotic system, which can produce four-wing, six-wing, eight-wing and ten-wing chaotic attractors. Several experimental circuits were also designed to show these multi-wing chaotic attractors.