  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
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.
