Analysis and Circuit Implementation of a Memristive Multi-Scroll Hyper-Chaotic System with Multi-Stability

In this paper, a hyperbolic tangential memristor simulator is designed, and a new memristor-based multi-scroll hyper-chaotic system is designed based on this memristor. The system equilibrium point is extended by controlling the designed sawtooth function, and the dynamic analysis of the system includes equilibrium point analysis, bifurcation diagram, Lyapunov exponential spectrum, coexisting attractors, and multi-stability analysis. The analysis reveals that under certain parameters, the system exhibits two positive Lyapunov indices. Notably, when different initial values are considered, the system demonstrates characteristics of multi-stability including homogeneous multi-stability, heterogeneous multi-stability, and extreme multi-stability. Furthermore, transient coexisting attractors emerge when different initial values are used with specific system parameters. Finally, the corresponding chaotic circuit was designed and built based on the chaotic system, and the chaotic circuit was sampled, and the sampling results were consistent with the Matlab numerical simulation results.