Two-Dimensional Discrete Memristive Oscillatory Hyperchaotic Maps With Diverse Dynamics

Discrete memristor (DM) has been extensively used to enhance the complexity of simple chaotic maps due to its special nonlinearity. Yet, the chaotic properties inherent to DM have not been thoroughly explored. This article introduces a simple oscillatory term to the DM model and constructs four hyperchaotic maps. In these maps, the coupling of the ideal DM with the oscillatory term results in maps without fixed points, generating hidden hyperchaotic attractors. The introduction of the oscillatory term into DMs exhibits diverse dynamical behaviors, including coexisting bistable attractors, infinitely many homogeneously coexisting attractors, heterogeneously coexisting attractors, and symmetrically coexisting attractors. The performances of the sequences generated by these maps are evaluated, and they are successfully applied to the design of pseudorandom number generators (PRNGs). The research results demonstrate that the outputs of all four maps, as well as the pseudorandom numbers generated by the PRNG, exhibit high randomness. Finally, a hardware platform is constructed to successfully implement these maps.