基于阈值控制策略的Filippov神经元模型的动力学及多稳态分析

Dynamics and multistable analysis of Filippov neuron model based on threshold control strategy

电磁感应在调节神经元的电活动、兴奋性和双稳态结构中起着关键作用.基于电磁场影响下的HR神经元模型(EMFN模型),引入了一种以膜电位为阈值的不连续控制策略,实现了电磁场对神经元系统的调控作用,并由此建立了Filippov EMFN神经元模型.首先,结合Matcont软件分析了2个子系统平衡点的存在性与稳定性;其次,借助双参数分岔分析详细探讨了其双稳态区域及内部机制;最后,结合快慢动力学分析,进一步探究了包括滑膜段、滑动分岔等一系列复杂的滑膜动力学及多稳态性的产生机理.数值仿真结果表明,EMFN模型在阈值控制策略的影响下会产生相应的滑膜极限环和滑膜簇放电等行为.所得结果为控制电磁场对生物神经系统的影响,以及探求神经性疾病的调控机理提供了思路.

Electromagnetic induction plays a key role in regulating the electrical activity,excitability and bi-stable structure of neurons.In this paper,based on the HR neuron model(EMFN model)under the influence of electromagnetic field,a discontinuous control strategy with the threshold ofmembrane potential is introduced to realize the regulating effect of electromagnetic field on neuron system,and thus the Filippov EMFN neuron model is established.Firstly,the existence and stability of equilibrium points of two subsystems are analyzed by using Matcont software.Secondly,the bi-stable region and its internal mechanism are discussed in detail by means of two-parameter bifurcation analysis.Finally,a series of complex sliding mode dynamics,including sliding segmentsand sliding bifurcations,and the mechanism of multi-stability,are further explored with the help of fast-slow variable dissection method of dynamics analysis.The simulation results show that the EMFN model can produce the corresponding sliding limit cycle and sliding bursting under the influence of thethreshold control strategy.The results provide ideas for controlling the effects of electromagnetic field on biological nervous system and exploring the regulation mechanism of neurological diseases.