Filippov FitzHugh-Nagumo Neuron Model with Membrane Potential Threshold Control Policy

In this paper, a novel FitzHugh-Nagumo (FHN) neuron model with membrane potential threshold control policy is proposed. As the membrane potential threshold control policy is a switching control policy, our proposed model is a Filippov system, which is different from the existing FHN model. For this model, first, the sliding segments and sliding regions are investigated. Then, based on the obtained sliding regions, we discuss the null-clines and the existence conditions of various equilibria such as regular equilibrium, virtual equilibrium and boundary equilibrium. By choosing the membrane potential threshold as the bifurcation parameter, the boundary node bifurcation, pseudo-saddle-node bifurcation and the global touching bifurcation are investigated by using numerical techniques. Furthermore, the effectiveness and correctness of the proposed FHN model with membrane potential threshold control policy are verified by circuit simulation. Numerical examples show that the membrane potential threshold guided switching may cause complex dynamics.