Parallel bi-memristor hyperchaotic map with extreme multistability

Abstract

Discrete memristors can be used to construct chaotic and hyperchaotic mapping models by self-feedback or coupling method, but these constructed maps do not have multistability or extreme multistability. Towards this end, by connecting two identical discrete memristors in parallel, this paper presents a novel parallel bi-memristor hyperchaotic map using the self-feedback method. This map has a plane fixed point set and its stability is entirely determined by memristor initial states. The control parameters-reliant hyperchaotic behaviors and the initial states-reliant coexisting behaviors are disclosed using several numerical methods. Complex dynamical behaviors closely relative to memristor and non-memristor initial states are demonstrated, indicating the occurrence of extreme multistability. Besides, a digital hardware platform is developed and the experimental results are captured to well validate the numerical ones. Consequently, the presented parallel bi-memristor map can display hyperchaotic dynamics and it is flexible to show extreme multistability.