Complex firing activities and bifurcations in memristor-coupled Hindmarsh–Rose neuron

Abstract

Due to the unique synaptic plasticity and memory effect, a memristor can not only mimic biological synapses but also characterize the influence of external electromagnetic radiation. In this paper, a ReLU-type non-ideal memristor with a simple structure is first coupled to a classical three-dimensional Hindmarsh–Rose neuron to describe the electromagnetic induction effect, which can show period-doubling, period-adding, and saddle-node bifurcations by varying the coupling strength of the memristor. Furthermore, complex discharge behaviors of the system, including bursting discharge and spiking discharge, are exhibited, and some coexisting discharge modes associated with initial values are also presented. Finally, an analog circuit scheme consuming fewer circuit components is designed, and it was found that the experimental results are consistent with the numerical results.