A Novel Nonideal Flux-Controlled Memristor Model for Generating Arbitrary Multi-Double-Scroll and Multi-Double-Wing Attractors

Abstract

This paper proposes a novel nonideal flux-controlled memristor model with a multipiecewise linear memductance function, which can be used to construct a memristive multi-scroll or multi-wing chaotic system. Importantly, arbitrary multi-double-scroll and multi-double-wing attractors can be generated depending on this memristor model directly and without the need to change the original nonlinear terms of the system. Another highlight is that the odd or even number of the double-scroll and double-wing attractors can also be freely controlled by the memristor model. To further illustrate these unique features, by introducing the memristor model into two classical chaotic systems, i.e. Jerk system and Lorenz system, multi-double-scroll and multi-double-wing chaotic attractors are obtained respectively. The formation mechanism of the multi-double-wing and multi-double-scroll attractors is also discussed. Moreover, the randomness of the chaotic binary sequences generated by the proposed memristor model is tested by the National Institute of Standards and Technology test suite. The tested results are better than those of the well-known Lorenz system. Furthermore, the corresponding circuits are constructed. The experimental results and the numerical simulations coincide well with each other, showing the effectiveness and feasibility of the proposed memristor model.