Dynamics and propagation of memristive neuron models with electrical fields

Manufactured devices from thermoelectrical semiconductor materials have shown that the carrier concentration in the metal-insulator channel structures is strongly associated with the history of the applied voltage. The devices have attracted a great deal of attention as promising elements in brain-inspired circuits. In this paper, a memristive model based on the carrier concentration is proposed. We derive a theoretical semi-analytical solution for the current-voltage curve with a pinched hysteresis loop consistently obtained by the finite difference numerical calculation. The memristive model appears a shaking negative resistance, which is relative to the generation of complex oscillating patterns. Further, we propose a Hodgkin-Huxley-type circuit where the memristive current takes on the role of nonlinear ionic currents. Constructed memristive neuron-like models with an electric field effect can produce complex oscillating modes involving periodic, bursting, and chaotic firings. The propagations and spatiotemporal dynamics are exhibited through the finite difference numerical method. The obtained result provides a biophysical mechanism for the memristive neuron-like model inspired by semiconductors and further highlights opportunities for investigating coupled memristive networks for developing adaptive systems applied to multiscale neuromorphic computations.