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

Wei Yi ^*

• HRL Laboratories (United States), Malibu, United States

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-tometal phase transition. This approach allows a connection between the dynamical behaviors of a Mott memristor and its physical device parameters as well as a complete mapping of the locally passive and edge of chaos domains in the frequency and current operating parameter space, which could guide materials and device development for neuromorphic circuit applications.We also examined the applicability of local analyses on a second-order relaxation oscillator circuit that consists of a voltage-biased vanadium dioxide memristor coupled to a parallel reactive capacitor element and a series resistor. 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 a supercritical Hopf-like bifurcation from an unstable spiral to a stable limit cycle, with each of the three circuit parameters acting as a bifurcation parameter. The abruptive growth in the limit cycle resembles the Canard explosion phenomenon in systems exhibiting relaxation oscillations. Finally, we show that experimental limit cycle oscillations in a vanadium dioxide nano-device relaxation oscillator match well with SPICE simulations built upon the compact model.