Bursting and spiking activities in a Wilson neuron circuit with memristive sodium and potassium ion channels

The marvelous Wilson neuron model involves sodium and potassium ion currents, which offer great significance in generating firing activities. This paper firstly deduces that the sodium ion currents can be characterized by a locally active memristor (LAM) and the potassium ion current meets the definition of passive memristor. Thereafter, a memristive Wilson neuron circuit with memristive sodium and potassium ion channels is built and its equilibrium state stability is disclosed. Dynamical explorations display that the memristive Wilson neuron circuit can generate abundant periodic bursting activities with different periodicities under low-frequency stimulus and chaotic/periodic spiking activities under high-frequency stimulus. Particularly, the bifurcation mechanisms for generating the periodic bursting behaviors are uncovered, they are Hopf/fold and fold/fold bifurcations. Besides, the memristive Wilson neuron circuit can generate chaotic and periodic bubbles with Type-I. To physically confirm these periodic bursting and chaotic/spiking activities, a discrete circuit component-based hardware experiment is executed. The experimental results effectively addressed the validity of the numerical explorations and further exhibit the effectiveness of the memristive Wilson neuron circuit in reproducing neuron bursting and spiking activities.