Multistability, Noise Induced Transitions, and Stochastic Resonance in a Nonlinear Oscillator With a Nonvolatile Memristor

We investigate multistability, noise-induced transitions, and stochastic resonance in a second-order nonlinear oscillator incorporating a nonvolatile memristive device. The memristor provides a programmable nonlinear conductance, enabling bistable dynamics with two asymptotically stable equilibrium points separated by a saddle. Under periodic excitation, the system exhibits coexisting limit cycles, period-doubling cascades, boundary crises, and transitions to chaos. Lyapunov exponent analysis reveals repeated crossings of the edge-of-chaos regime, where the largest nonzero exponent approaches zero, marking a balance between stability and sensitivity to perturbations. The effects of additive Gaussian white noise are analyzed by reformulating the dynamics in terms of an effective potential landscape, where noise induces random transitions between coexisting attractors. Transition rates are accurately described in the weak-noise regime by the Eyring–Kramers formula. When periodic forcing and noise act jointly, the system exhibits stochastic resonance, with optimal synchronization occurring when the forcing period matches the mean noise-induced transition time. These results demonstrate that memristor-based nonlinear circuits naturally operate near critical dynamical regimes and provide a compact hardware platform for studying noise-assisted computation and edge-of-chaos dynamics in neuromorphic systems.