A memristive conservative chaotic circuit with two different offset boosting behaviors

Abstract

Recent studies have shown that more complex dynamics could be observed if memristors are coupled into nonlinear circuits. To date, however, far too little attention has been paid to memristor-based high-dimensional conservative systems. Previous research on the low-dimensional mem-element system has suffered from a paucity of rich dynamical characteristics. In addition, the physical implementation of conservative systems requires higher accuracy than dissipative ones, and no DSP implementation of a memristor-based conservative system is available. In this paper, a high-dimensional memristive conservative system is built by coupling the linear resistance of a conservative chaotic circuit with a flux-controlled memristor. Compared to the existing conservative systems, the proposed system exhibits a variety of quasi-periodic topologies and has two offset boosting behaviors. One of the constant variable offset boosting also presents meaningful parameter space expansion characteristics. And the other initial offset boosting exhibits homomorphic and heteromorphic multistability properties. Moreover, our work also reveals that transient chaos is the route to chaos in conservative systems. Finally, analog circuit simulation and DSP-based digital circuits verify the correctness of the numerical calculation and the physical implementations of the system.