Extreme multistability in a double-memristors-based chaotic system

Abstract A novel double-memristor-based chaotic system (DMCS) is proposed in this paper to address limitations in traditional chaos generation methods. Two identical memristors are introduced into the first and third dimensions of a chaotic system, creating a unique platform for investigating extreme multi-stability induced by the memory characteristics of the memristors. Diverse coexisting attractors are observed, with variations in initial conditions resulting in shifts in both the position and size of the attractors. Additionally, cross-dimensional control of multistability is achieved, where the stability in one dimension is influenced by initial values in other dimensions, leading to symmetric attractor arrangements under specific conditions. An inverse regulation of the attractor oscillation range is enabled by adjusting the memristor coupling strength, providing a novel chaotic signal tuning mechanism. The system’s chaotic dynamics are validated through a circuit implementation in Multisim, where fundamental behaviors predicted by theoretical analysis are confirmed. A pseudo-random number generator (PRNG) based on the DMCS is developed, demonstrating exceptional randomness as verified by rigorous testing.