Effects of non-ideal characteristics of memristor on the complex dynamics of memristor-coupled discrete Rulkov...

As an emerging nonlinear electronic device, the memristor has become a key element for constructing neuromorphic systems owing to its properties of nonvolatile memory, asymmetry, negative differential resistance (NDR), and tunable synaptic plasticity. This paper develops a discrete Rulkov neuron system driven by a continuous memristor based on a triangularly modulated nonlinear memristor model. The work systematically explores how memristive characteristics regulate complex dynamical behaviors from both the device and system perspectives. At the device level, experiments on current-voltage (i-v) hysteresis loops and analyses of NDR reveal several non-ideal characteristics of the memristor, including memory saturation, symmetry breaking, and locally active regions. At the system level, memristive parameters, asymmetry, and NDR effects are shown to induce complex spatiotemporal structures such as synchronization symmetry breaking, multistability, solitary states, and chimera states. Moreover, the coupling between the memory-saturation gating window and the rate of parameter variation can trigger rate-induced tipping (R-tipping) in the system. Further investigation uncovers quantitative correlations between the geometric features of the memristor's i-v characteristics (loop area, intersection angle, and NDR proportion) and the system's complexity metrics, including the Lyapunov exponent, permutation entropy, and recurrence quantification analysis. These findings elucidate the multilevel modulation mechanisms through which the non-ideal properties of the continuous memristors shape the complex dynamics of discrete neural systems, offering new theoretical insights and engineering guidance for the design of highly robust memristive neuromorphic chips and chaos-based secure communication.