耦合Rulkov神经元的复杂动力学行为  

Complex Dynamic Behavior of Coupled Rulkov Neurons

作　　者：薛睿 张莉[2] 安新磊[1] XUE Rui;ZHANG Li;AN Xinlei(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China;Department of the Basic Courses,Lanzhou Institute of Technology,Lanzhou 730050,China)

机构地区：[1]兰州交通大学数理学院,兰州730070 [2]兰州工业学院基础科学部,兰州730050

出　　处：《吉林大学学报（理学版）》2024年第4期971-979,共9页Journal of Jilin University:Science Edition

基　　金：甘肃省自然科学基金重点项目(批准号:23JRRA861);兰州工业学院青年科技创新项目(批准号:2021KJ-08)。

摘　　要：基于混沌的Rulkov神经元模型,考虑2个相同神经元在电耦合下的情形,通过数值计算对耦合Rulkov神经元模型进行双参数分岔分析,并借助单参数分岔图以及最大Lyapunov指数图进一步验证其分岔模式.结果表明:耦合Rulkov神经元模型呈倍周期分岔道路、拟周期道路以及阵发性道路3条典型的混沌路径;该模型具有伴有混沌的加周期分岔现象;随着耦合强度的增加,耦合Rulkov模型呈更复杂的动力学行为.Based on the chaotic Rulkov neuron model,the two-parameter bifurcation analysis of the coupled Rulkov neuron model was carried out through numerical calculations by considering the situation of two identical neurons under electrical coupling,and the bifurcation mode was further validated by using the one-parameter bifurcation diagrams and the maximum Lyapunov exponent diagrams.The results show that the coupled Rulkov neuron model exhibits three classic chaotic paths:period-doubling bifurcation path,quasi-periodic bifurcation path,and intermittency path.The model presents a period-adding bifurcation phenomena accompanied by chaos.The coupled Rulkov neurons model exhibits more complex dynamical behavior as the coupling strength increases.

关 键 词：Rulkov神经元 电耦合 双参数分岔分析 最大LYAPUNOV指数 混沌道路 

分 类 号：O415.5[理学—理论物理]