Nonlinear dynamics and stability analysis of locally active Mott memristors using a physics-based compact model - Yi, Wei (Frontiers in Materials, 2025)
Locally active memristors (LAMs) are a class of emerging nonlinear dynamic circuit elements that hold promise for scalable yet biomimetic neuromorphic circuits. Starting from a physics-based compact model, we performed small-signal linearization analyses and applied Chua’s local activity theory to a one-dimensional, locally active vanadium dioxide Mott memristor based on an insulator-to-metal phase transition. This approach establishes a connection between the dynamical behaviors of a Mott memristor and its physical device parameters, enabling a complete mapping of the locally passive and edge-of-chaos domains in the frequency and current operating parameter space. This mapping could guide materials and device development for neuromorphic circuit applications. We also examined the applicability of local analyses to a second-order relaxation oscillator circuit, which consists of a voltage-biased vanadium dioxide memristor coupled to a parallel reactive capacitor element and a series resistor. Chua’s local activity criteria allows a mapping of this second-order system’s dynamics and stability in the frequency and circuit parameter space, which is essentially a phase diagram for complexity. It shows that the coupling increases both the system’s dimension and its dynamical complexity and creates a locally active and unstable region to host instabilities and persistent oscillations. We show that global nonlinear techniques, including nullclines and phase portraits, provide further insights into instabilities and persistent oscillations near non-hyperbolic fixed points. Specifically, we observe a supercritical Hopf-like bifurcation, where an orbitally stable limit cycle emerges as a new attractor when a stable spiral transitions to an unstable one, with each of the three circuit parameters acting as a bifurcation parameter. The abrupt growth of the limit cycle resembles the Canard explosion phenomenon observed in systems exhibiting relaxation oscillations. Finally, we show that experimental limit cycle oscillations in a vanadium dioxide nano-device relaxation oscillator closely match SPICE simulations based on the compact model.