Nonlinear dynamics and stability analysis of locally-active Mott memristors using a physics-based compact model

Locally-active memristors 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 allows a connection between the dynamical behaviors of a Mott memristor and its physical device parameters, which could guide materials and device development for neuromorphic circuit applications. We also examined the applicability of local analyses on a second-order circuit consists of a vanadium dioxide memristor coupled to an external reactive element, specifically a parallel capacitor. Finally, we show that global nonlinear techniques including nullclines and phase portraits provide insights on instabilities and persistent oscillations near non-hyperbolic fixed points, such as the creation of a stable limit cycle in a supercritical Hopf bifurcation, with some of the bifurcation characteristics distinctive from the general predictions.