A multi-wing butterfly chaotic system and its implementation

It has been a common brief that the principle for generating multi-wing attractor from a Lorenz-like chaotic system is to construct an even symmetric function for the system. In this pursuit, research effort on exploring the possibility of using non-even symmetric function is scant, if any. This paper attempts to reveal the intrinsic relation between such a system function and its generated multi-wing attractor in a chaotic system. It will be shown that a rather simple asymmetric function applying to the Shimizu-Morioka system can indeed generate a multi-wing butterfly chaotic attractor. Then, some basic properties, compound structure, bifurcation diagram, Lyapunov exponent spectrum, and dynamical analysis of the new chaotic system are investigated in detail. Finally, an electronic circuit is designed and its experimental results are presented, which well match the numerical simulation results, thereby verifying the feasibility of the new method. Copyright (c) 2017 John Wiley & Sons, Ltd.