电磁辐射下HR神经元模型的分岔分析  

Bifurcation Analysis on HR Neuron Models Under Electromagnetic Radiation

作　　者：乔帅 张莉 安新磊[1] 王红梅 张薇 QIAO Shuai;ZHANG Li;AN Xinlei;WANG Hongmei;ZHANG Wei(School of Mathematics and Physic,Lanzhou Jiaotong University,Gansu Lanzhou 730070,China;Department of the Basic Courses,Lanzhou Insitute of Technology,Gansu Lanzhou 730050,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070 [2]兰州工业学院基础学科部,甘肃兰州730050

出　　处：《河北师范大学学报（自然科学版）》2019年第4期306-312,共7页Journal of Hebei Normal University：Natural Science

基　　金：甘肃省自然科学基金(17JR5RA096);兰州工业学院青年科技创新项目(17K-016)

摘　　要：运用理论与仿真相结合的方法,分析了电磁感应下改进的HR神经元模型的动力学特征.由于系统的关键参数与外刺激电流的变化对系统动力学行为有重要的影响,因此分析了外界刺激电流对系统平衡点分布的影响,发现了多值平衡点区域.在此基础上,对系统进行鞍结分岔分析,探讨了关键参数对系统临界鞍结点分布的影响,同时分析了系统Hopf分岔及其分岔类型与分岔出的周期解的稳定性,并与数值模拟相结合验证了上述的理论分析,从而揭示了系统所具备的复杂的放电特征.The dynamics of the improved HR neuron model under electromagnetic induction is analyzed by combining theory with simulation.Considering the key parameters of the system and the change of external stimulation current have an important influence on the dynamic behavior of the system,the influence of external stimulus current on the equilibrium point distribution of the system was analyzed and finds the multi-value equilibrium point region was found in this paper.On this basis,the saddle-node bifurcation analysis of the system is carried out,and the influence of key parameters on the critical saddle node distribution of the system is discussed.At the same time,the stability of the system Hopf bifurcation and its bifurcation type and the bifurcation periodic solution are analyzed.Combined with numerical simulation,the above theoretical analysis is verified,which reveals the complex discharge characteristics of the system.

关 键 词：多值平衡区 鞍结分岔分析 临界鞍结点 Hopf分岔分析 

分 类 号：O193[理学—数学] O441[理学—基础数学]