多巴胺能神经元模型的分岔分析与同步研究  

Bifurcation analysis and synchronization of dopaminergic neuron model

作　　者：林心怡 刘深泉[1] 宋健 LIN Xinyi;LIU Shenquan;SONG Jian(School of Mathematics,South China University of Technology,Guangzhou 510640,China)

机构地区：[1]华南理工大学数学学院,广东广州510640

出　　处：《广西大学学报（自然科学版）》2024年第1期204-217,共14页Journal of Guangxi University（Natural Science Edition）

基　　金：国家自然科学基金项目(11872183)。

摘　　要：为了研究多巴胺能神经元模型的动力学性质,增进对模型由小电导钙激活钾通道阻断介导的反常簇行为的了解,利用变量相关性进行模型降维并构建四维简化多巴胺能神经元模型以及两神经元电突触与化学突触耦合模型,通过分岔理论与数值计算方法研究简化模型的动力学性质以及耦合模型的放电特性和同步转迁规律。结果表明:在不同参数组合下,简化模型存在由加周期分岔转迁至混沌状态的动力学现象;电突触耦合模型存在逆加周期分岔现象,在一定刺激电流下,改变耦合强度可诱导电突触耦合模型达到簇同步或静息同步状态;化学突触耦合模型存在复杂的混合振荡现象,在一定耦合强度下,较强的刺激电流或较大的突触逆转电位可诱导化学突触耦合模型达到完全同步状态。多巴胺能神经元耦合模型的同步状态不仅受耦合强度的影响,还受到外界刺激电流以及模型参数的影响。To study the dynamic properties of dopaminergic neuron model and know more about the abnormal bursting behavior mediated by small conductance calcium activated potassium channel blocking in the model,the model dimension was reduced by using variable correlation,and a four-dimensional dopaminergic neuron model and a coupling system of two neuron with electrical synapse and chemical synapse were constructed.The dynamical properties of the model and the discharge characteristics and the conditions for the system to realize the synchronization were analyzed by bifurcation theory and numerical calculation method.The results show that under different parameter combinations,the model all has the dynamic phenomenon of the transition from adding periodic bifurcation to chaotic state.There is a bifurcation phenomenon of the inverse adding period in the electrical coupling system.Under certain stimulation current,the coupling strength can be changed to induce the electrical coupling system to reach bursting synchronization or resting synchronization state.The chemical coupling system has complex mixed oscillation phenomenon.Under certain coupling strength,the chemical coupling system can be induced to fully synchronization by strong stimulation current or large synaptic reversal potential.The synchronization state of dopaminergic neuronal coupling system is affected not only by coupling strength,but also by stimulation current and model parameters.

关 键 词：多巴胺能神经元 分岔理论 耦合 同步 

分 类 号：O193[理学—数学] Q189[理学—基础数学]