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.

在本文中，提出了一种具有膜电位阈值控制策略的新型 FitzHugh-Nagumo (FHN) 神经元模型。由于膜电位阈值控制策略是一种切换控制策略，我们提出的模型是一个 Filippov 系统，与现有的 FHN 模型不同。对于该模型，首先研究滑动段和滑动区域。然后，基于获得的滑动区域，我们讨论了零斜线和各种平衡如规则平衡、虚平衡和边界平衡的存在条件。通过选择膜电位阈值作为分叉参数，利用数值技术研究了边界节点分叉、伪鞍节点分叉和全局接触分叉。此外，通过电路仿真验证了所提出的具有膜电位阈值控制策略的 FHN 模型的有效性和正确性。数值例子表明，膜电位阈值引导的切换可能会导致复杂的动力学。