A nonvolatile multistable discrete locally active memristor and its switching dynamics

Nonvolatile multistable memristors can switch between memory states when subjected to appropriate excitation sources. However, the switching dynamics of discrete memristors and underlying state-switching mechanism have not yet been reported. To address this gap, a discrete butterfly memristor (DBM) family model is proposed, exhibiting multistability, nonvolatility, local activity, and edge-of-chaos, as revealed by its nonlinear dynamics. Furthermore, the switching mechanism of equilibrium states in generic discrete memristor is theoretically derived, and the switching dynamic characteristics of the DBM are numerically investigated, including four unidirectional switching scenarios induced by single voltage pulses and two successful bidirectional switching scenarios triggered by bipolar periodic voltage pulses. Additionally, a DBM-based neuron map (DNM) incorporating the magnetic induction effect is introduced. Numerical simulations suggest that the DNM can generate bifurcations with symmetric and staircase structures, cloned chaotic and periodic attractors, offset-boosted coexisting attractors, and coherence resonance. Moreover, hardware experiments on Field Programmable Gate Array (FPGA) confirm the physical feasibility of the DNM model. Ultimately, an image compression and encryption scheme is developed to expand the practical computational applications for the DNM.