Memristor initial-boosted extreme multistability in the novel dual-memristor hyperchaotic maps

In the involvement of discrete memristors with periodic trigonometric memristances, the existing memristor maps can present initial-boosted bistability. However, no recent studies have explored the initial-boosted extreme multistability. To this end, by paralleling two discrete memristors with sine and cosine memristances, this paper constructs two novel dual-memristor hyperchaotic maps: the homogeneous sine-sine discrete memristor (SSDM) map and the heterogeneous sine-cosine discrete memristor (SCDM) map. The considered maps have plane fixed points and their stability distributions are partitioned in the coupling strength as well as the memristor initial condition planes according to the non-one eigenvalues. This paper further investigates the coupling strength-related dynamical behaviors and especially memristor initial-boosted coexisting bifurcations using numerical methods such as bifurcation diagrams, Lyapunov exponents, phase portraits, and basins of attraction. The theoretical and numerical results show that the SSDM and SCDM maps can not only generate complicated hyperchaotic behaviors but also exhibit remarkable initial-boosted extreme multistability; that is, an infinite number of coexisting heterogeneous attractors can self-reproduce along the line and plane under the control of the memristor initial conditions. Additionally, a microcontroller-based digital circuit platform is developed to verify the dynamical behaviors explored through numerical methods. Finally, the applications in pseudo-random number generators improve the practical values of the proposed maps.