周期激励下的前包钦格呼吸神经元的簇振荡现象研究  

The Study of Bursting Oscillation for Pre-B?tzinger Respiratory Neuronswith Periodic Excitation

作　　者：孟盼 陈艳美 董健卫 MENG Pan;CHEN Yan-mei;DONG Jian-wei(College of Medical Information Engineering,Guangdong Pharmaceutical University,Guangzhou 510006,China;School of Mathematics and Systems Science,Guangdong Polytechnic Normal University,Guangzhou,510665,China)

机构地区：[1]广东药科大学医药信息工程学院,广州510006 [2]广东技术师范大学数学与系统科学学院,广州510665

出　　处：《数学的实践与认识》2020年第8期149-157,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11402057,11801097);广东省普通高校青年创新人才项目(2014KQNCX137);广东省教育厅特色创新项目(2018KTSCX125);广东药科大学创新强校工程资助项目(2017JGXM-MS38)。

摘　　要：研究周期激励作用下的非自治前包钦格呼吸神经元模型,结果表明当外界激励频率与系统固有频率存在着量级差距时,系统可以产生典型的簇放电模式.由于激励频率远小于系统的固有频率,因此将整个周期激励项视为慢变参数,从而可以利用稳定性分析理论研究慢变参数变化下的平衡点的分岔类型,进一步应用快慢动力学分析方法给出簇模式产生的动力学机理.本文的结果说明外界激励对神经元的动力学行为有着重要影响,为进一步揭示呼吸节律的产生机制提供了重要帮助.In this paper,the non-autonomous Pre-B?tzinger respiratory neuron model with periodic excitation is studied.The results show that when there is a order gap between the exciting frequency and the natural frequency of the system,the system can generate typical bursting clusters.Since the exciting frequency is far less than the natural frequency of the system,thus the whole periodic term can be regarded as a slow-varing parameter.With the variation of the slow-varing parameter,the bifurcation type of the equilibrium point is explored by using the stability analysis theory and then fast slow dynamic analysis method is further applied to give the burtsing generation mechanism.The results of this paper show that the external stimulus have an important influence on the dynamic behavior of neurons,which provides important help for further revealing the mechanism of respiratory rhythm.

关 键 词：前包钦格 电流反馈 簇模式 快慢动力学分析 分岔 

分 类 号：O175[理学—数学] R338[理学—基础数学]