A Universal Discrete Memristor With Application to Multi-Attractor Generation

Discrete memristors have been employed in discrete maps for the purpose of chaos generation and regulation. In this paper, a novel universal model for discrete memristors is proposed to generate multi-attractors. The classical Hénon map and Rulkov neuron are chosen as two examples to verify the effectiveness of the proposed memristor. Coexisting homogeneous attractors are identified in the phase space by memristor-induced offset boosting. An arbitrarily desired number of coexisting attractors is extracted by the appropriate feedback strength of the memristor. What adds further interest to this case is that the amplitude is rescaled by a memristor-related parameter that works well over an infinite range. Number-related parameters are extracted to rescale the oscillation range of the chaotic signals. Moreover, CH32-based circuit implementation is built, which aligns with numerical simulation results. Finally, coexisting homogeneous chaotic signals are tested to explore their robust performance in the application of pseudo-random number generator.