Morris-Lecar模型双参数分岔分析  

Two-parameter Bifurcations of Morris-Lecar Model

作　　者：卢裕木 丁学利[1] 李群宏[1] 

机构地区：[1]广西大学数学与信息科学学院,广西南宁530004

出　　处：《海南师范大学学报（自然科学版）》2016年第3期237-241,共5页Journal of Hainan Normal University（Natural Science）

基　　金：广西自然科学基金项目(2013GXNSFAA019017)

摘　　要：Morris-Lecar(M-L)模型是一个重要的神经元模型.当适当调整参数时,M-L模型展示出许多复杂的动力学行为.文章针对M-L模型,利用双参数分岔分析并结合数值仿真的方法,研究了双参数平面上神经元电活动的存在区域及神经元电活动之间的转迁机制,实现了用同一个神经元模型模拟四种单参数分岔(超临界Hopf分岔、亚临界Hopf分岔、不变环上的鞍-结分岔和鞍同宿轨分岔)行为之间的转迁.同时,还考虑了在双参数分岔点附近极限环的幅值和共存区间的大小问题,为进一步研究分岔点附近的随机动力学机制提供了理论基础.Morris-Lecar model is an important neuron model. When adjusting the parameters properly, Morris-Lecar model can display a number of complex dynamic behaviors. Using the method of two-parameter bifurcation analysis, combined with numerical simulation, the existent area in the two-parameter plane as well as the transition mechanism of the neural firing actions are studied for the Morris-Lecar model, and achieves the transitions of four one-parameter bifurcations（supercritical hopf bifurcation, subcritical hopf bifurcation, saddle-node on invariant circle and saddle homoclinic orbit bifurcation）within only one single Morris-Lecar model. Additionally, the amplitude of the limiting cycle and co-existing intervals near the two-parameter bifurcation point are also considered. This paper provides a theoretical basis for further research of stochastic dynamic mechanism near the bifurcation point.

关 键 词：神经元 双参数分岔 HOPF分岔 不变环上的鞍-结分岔 鞍同宿轨分岔 

分 类 号：O241.6[理学—计算数学]