A novel 5D memristor conservative chaotic system with multiple forms of hidden flows

Abstract

Abstract Memristor is one of the basic circuit elements commonly used in circuit model analysis. More complex dynamic characteristics can be observed by coupling memristor into nonlinear circuit. However, there is relatively little attention paid to high-dimensional conservative chaos based on memristors up to now. In this paper, a five-dimensional memristor conservative chaotic system is built after the introduction of the memristor into conservative chaotic system. There is no equilibrium point in this system and the phase trajectory produced by it has hidden properties. Its conservatism is analyzed by bifurcation diagram, Lyapunov exponent spectrum and divergence. The phase trajectory will change with the change of parameters, which Poincaré mapping also verified these dynamic behaviors. In addition, hidden extreme multistability and initial value offset boosting behavior are also found in this system. It is to be noted that this behavior is less in memristor conservative chaotic system without equilibrium points. At the same time, a new transient transition behavior is observed. By introducing spectral entropy algorithm, the complexity of sequences is analyzed and compared with the existing literature. The results show that the system has higher complexity. Finally, the systematic analogous circuit is designed and built whose results are consistent with the MATLAB numerical simulation results, which has laid a solid foundation for the practical application of the system in engineering.