DC operating points of Mott neuristor circuits

In 1960 Hewitt Crane conceptualized neuristors as electronic logic networks that could mimic action potential generation by biological neurons. In 2012 Mott memristors were presented as nano-scale electronic devices for physically constructing neuristor networks. Both the original Mott memristor model and the simplified model presented in 2020 are stiff nonlinear first-order ordinary differential equations (ODEs) that describe the voltage controlled threshold switching and current controlled negative differential resistance, attributed to a Mott insulator-to-metal phase transition. By design, a Mott neuristor contains two identical Mott memristors plus linear resistors and capacitors (no inductors), which enables alternating threshold switching by the memristors to generate periodic (AC) output voltage spikes in response to a DC current or voltage input. This paper presents a steady-state analysis of dynamic neuristor models, including four-, five-, and six-state variables (each of which is a system of first-order ODEs involving the states) based on the original phenomenological model of the Mott memristor. Specifically, it reveals the unique stable operating points that occur for applied currents or voltages below the amounts needed to induce resistive switching. These DC operating points represent the physically meaningful "OFF" states for the circuit when the neuristor does not output voltage spikes. Jacques Hadamard's mathematical criteria for a well-posed physical model (existence, uniqueness, continuity, stability) motivated the search for these DC operating points (OFF states), which are needed for efficiently initializing neuristor models before conducting dynamic neuristor simulations. The key result of our analysis is the neuristor steady-state eq. (29) which is useful for understanding neuristor OFF states as well as the role of negative-differential resistance (NDR) in the operation of the Mott memristor model and neuristor circuits. In addition to the steady-state analysis, three numerical examples of dynamic neuristor circuit operation are also given and MATLAB code for the dynamic four-state model is available for interested readers.