电磁感应下神经元模型的放电模式及分岔分析  

Firing patterns and bifurcation analysis of neural model under electromagnetic induction

作　　者：赵晴晴 刘深泉 孟盼 ZHAO Qing-qing;LIU Shen-quan;MENG Pan(School of Mathematics,South China University of Technology,Guangzhou 510641,Guangdong,China;School of Basic Courses,Guangdong Pharmaceutical University,Guangzhou 510006,Guangdong,China)

机构地区：[1]华南理工大学数学学院,广东广州510641 [2]广东药科大学医药信息工程学院,广东广州510006

出　　处：《云南大学学报（自然科学版）》2023年第6期1238-1248,共11页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金(11872183,11572127).

摘　　要：在类Hindmarsh-Rose神经元模型的基础上,考虑了磁通量和电磁感应对细胞膜的影响,构建了一个四维模型.通过峰峰间距分岔图发现模型产生复杂的动力学现象,即逆加周期分岔、逆倍周期分岔及倍周期分岔导致混沌.利用快慢动力学分析得到了4种不同的簇放电模式.通过快速子系统的余维2分岔分析了不同簇放电模式之间的转迁机制.最后全系统的余维2分岔给出更多分岔信息.In this paper,based on the modified Hindmarsh-Rose neuron model,we construct a fourdimensional model by considering the effect of magnetic flux and electromagnetic induction across cell membranes.According to the interspike intervals analysis,we find complex dynamic phenomena that inverse period-adding bifurcation,inverse period-doubling bifurcation and period-doubling bifurcation leading to chaos.We observe four kinds of bursting patterns by using fast-slow dynamics method.Then,we analyze the transition mechanisms between different bursting patterns through two-parameter bifurcation of the fast subsystem.Finally,codimension-two bifurcation analysis shows more details of bifurcation.

关 键 词：类Hindmarsh-Rose神经元模型 电磁感应 分岔 快慢动力学 簇放电模式 

分 类 号：O193[理学—数学] O441[理学—基础数学]