Memristor-coupled hyper-chaotic system with cosine memductance: heterogeneous/homogeneous extreme multistability and application to image encryption

Abstract Memristor-based systems can manifest extreme multistability, leading to the coexistence of infinitely many attractors. Nevertheless, chaotic systems that simultaneously exhibit both heterogeneous and homogeneous extreme multistability have rarely been studied. In this paper, a novel nine-dimensional (9-D) memristor-coupled hyper-chaotic system is introduced, and we delve into the intricate dynamical effects that arise from both memristor and non-memristor initial conditions within this system. Using the proposed model, we characterize the equilibrium set and stability distributions across three periodic intervals. Using multiple numerical methods, the initial-related heterogeneous and homogeneous extreme multistability are disclosed, alongside the elucidation of the mechanism underlying homogeneous extreme multistability. Moreover, to confirm the homogeneous extreme multistability, PSIM circuit simulations are conducted using a physically realized circuit. The proposed memristor-coupled hyper-chaotic system is employed for image encryption, with experimental results demonstrating its remarkable resistance against diverse potential attacks.