Firing pattern in a memristive Hodgkin–Huxley circuit: Numerical simulation and analog circuit validation

Abstract

Spiking firing patterns and their hardware implementation can assist us in exploring spike-based applications. The classical Hodgkin–Huxley circuit can generate spiking firing patterns, but it is hard to implement on analog platform because of the involvement of complex exponential nonlinearities for characterizing the sodium and potassium ion channels. To solve this issue, this paper proposes a second-order local active memristor (LAM) and a first-order LAM to respectively characterize the sodium and potassium ion channels in the Hodgkin–Huxley circuit, thereby obtains a memristive Hodgkin–Huxley circuit. Numerical simulations demonstrate that the memristive Hodgkin–Huxley circuit can generate abundant spiking firing patterns, i.e. periodic and chaotic spiking firing patterns. These abundant firing patterns can be effectively regulated by memristor- and stimulus-related parameters. Moreover, a PCB-based analog circuit employing off-the-shelf discrete circuit components is manually constructed and hardware experiments are executed. Experimental results captured from hardware measurements satisfactorily verify the numerically simulated spiking firing patterns and effectively exhibit the availability of the memristive Hodgkin–Huxley circuit in generating spiking firing patterns.