Hidden Coexisting Firing Patterns in a Hindmarsh-Rose Neuron Model with the Simplest Memristor

This work presents an improved three-dimensional Hindmarsh-Rose neuron model that takes into account the impact of electromagnetic induction. By employing magnetic flux to characterize this influence, the model demonstrates how electromagnetic induction produces membrane potential through a feedback memristive current. For this reason, the simplest memristor model, which has been reported in the literature, has been used. Interestingly the proposed neuron model does not possess equilibrium points and can exhibit hidden coexisting firing patterns. Numerical simulations have been conducted, unveiling the system’s dynamics and confirming that the proposed neuron model exhibits hidden coexisting firing patterns.