Memristors-coupled neuron models with multiple firing patterns and homogeneous and heterogeneous multistability

Memristors are extensively used to estimate the external electromagnetic stimulation and synapses for neurons. In this paper, two distinct scenarios, ideal memristor serves as external electromagnetic stimulation and locally active memristor serves as synapse, are formulated to investigate the impact of memristor on a 2D Hindmarsh-Rose neuron model. Numerical simulations show that the neuronal models in different scenarios have multiple burst firing patterns. The introduction of the memristor makes the neuronal model exhibit complex dynamical behaviors. Finally, the simulation circuit and DSP hardware implementation results validate the physical mechanism as well as the reliability of the biological neuron model.