Hidden coexisting firing patterns and bubble-like bifurcation in HR neuron model under electromagnetic induction

Abstract

When ions enter or leave cell membrane, action potentials are generated. The fluctuations or changes in action potential of neurons result in an extra electromagnetic field according to the Faraday’s law of induction. As a result, the electromagnetic field will contribute to generation of membrane potential as a feedback effect, which should not be ignored in neuron modeling. In this paper, a three-dimensional improved Hindmarsh–Rose neuron model considering the influence of electromagnetic induction is proposed, in which magnetic flux is used to describe the effect of electromagnetic induction that contributes to generation of membrane potential as a feedback memristive current. The improved neuron model has no equilibrium point and can present different types of hidden coexisting firing patterns. Besides, the neuron model can show bubble-like bifurcation modes by varying system parameters, which has not been reported in other Hindmarsh–Rose neuron models. Extensive numerical simulations are carried out and bifurcation analyses indicate that the proposed neuron model has a wide variety of hidden coexisting firing patterns and bifurcation modes. Finally, equivalent circuit is designed and performed in Pspice, and the simulation results are consistent well with the numerical ones.