A novel methodology for constructing a multi-wing chaotic and hyperchaotic system with a unified step function switching control**Project supported by the National Natural Science Foundation of China (Grant No. 61403143), the Natural Science Foundation of Guangdong Province, China (Grant No. 2014A030313739), the Science and Technology Foundation Program of Guangzhou City, China (Grant No. 201510010124), and the Excellent Doctorial Dissertation Foundation

Abstract

This paper aims at developing a novel method of constructing a class of multi-wing chaotic and hyperchaotic system by introducing a unified step function. In order to overcome the essential difficulties in iteratively adjusting multiple parameters of conventional multi-parameter control, this paper introduces a unified step function controlled by a single parameter for constructing various multi-wing chaotic and hyperchaotic systems. In particular, to the best of the authors’ knowledge, this is also the first time to find a non-equilibrium multi-wing hyperchaotic system by means of the unified step function control. According to the heteroclinic loop Shilnikov theorem, some properties for multi-wing attractors and its chaos mechanism are further discussed and analyzed. A circuit for multi-wing systems is designed and implemented for demonstration, which verifies the effectiveness of the proposed approach.