Dynamics of a memristive FitzHugh–Rinzel neuron model: application to information patterns

In this work, a memristive FitzHugh–Rinzel (mFHR) neuron prototype is introduced and investigated. The memristive device is exploited to simulate the impact of a magnetic radiation on the FitzHugh–Rinzel (FHR) neuron’s behavior. Depending on the strength of the electromagnetic induction and the intensity of the external stimulus, it is found that the model experiences self-excited firing activity. The two-parameter charts of the largest Lyapunov exponent and the bifurcation diagram investigation revealed the model exhibited hysteretic dynamics, which induced the coexistence of bifurcation of sets of parameters not yet revealed in such a model. The energy necessary to provide each firing activity in the proposed model is also estimated based on the Helmholtz theorem. Finally, results of the information patterns with a chain of 100 mFHR neurons are obtained by numerical calculations using Runge–Kutta (fourth-order) calculation method, which approaches solutions of the resulting dynamic equations. The spatiotemporal patterns and time series plots for membrane potential revealed regular localized structures made of alternate bright and dark bands identified as spikes, which are sensitive to external stimulation current, electromagnetic induction coefficients and synaptic coupling strength.