Multiple mixed state variable incremental integration for reconstructing extreme multistability in a novel memristive hyperchaotic jerk system with multiple cubic nonlinearity

Abstract

Memristor-based chaotic systems with infinite equilibria are interesting because they generate extreme multistability. Their initial state-dependent dynamics can be explained in a reduced-dimension model by converting the incremental integration of the state variables into system parameters. However, this approach cannot solve memristive systems in the presence of nonlinear terms other than the memristor term. In addition, the converted state variables may suffer from a degree of divergence. To allow simpler mechanistic analysis and physical implementation of extreme multistability phenomena, this paper uses a multiple mixed state variable incremental integration (MMSVII) method, which successfully reconstructs a four-dimensional hyperchaotic jerk system with multiple cubic nonlinearities except for the memristor term in a three-dimensional model using a clever linear state variable mapping that eliminates the divergence of the state variables. Finally, the simulation circuit of the reduced-dimension system is constructed using Multisim simulation software and the simulation results are consistent with the MATLAB numerical simulation results. The results show that the method of MMSVII proposed in this paper is useful for analyzing extreme multistable systems with multiple higher-order nonlinear terms.