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安新磊, 任雁澜. 基于阈值控制策略的Filippov Chay神经元动力学及其耦合同步. 力学学报, 2024, 56(4): 1-20. DOI: 10.6052/0459-1879-23-405
引用本文: 安新磊, 任雁澜. 基于阈值控制策略的Filippov Chay神经元动力学及其耦合同步. 力学学报, 2024, 56(4): 1-20. DOI: 10.6052/0459-1879-23-405
An Xinlei, Ren Yanlan. Dynamics of filippov chay neuron based on threshold control strategy and coupling synchronization. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(4): 1-20. DOI: 10.6052/0459-1879-23-405
Citation: An Xinlei, Ren Yanlan. Dynamics of filippov chay neuron based on threshold control strategy and coupling synchronization. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(4): 1-20. DOI: 10.6052/0459-1879-23-405

基于阈值控制策略的Filippov Chay神经元动力学及其耦合同步

DYNAMICS OF FILIPPOV CHAY NEURON BASED ON THRESHOLD CONTROL STRATEGY AND COUPLING SYNCHRONIZATION

  • 摘要: 细胞内外带电离子的连续泵送和传递产生的电磁感应效应对神经元的电活动及模态转换会产生一定的影响, 促使其展现出更加丰富的放电特性. 文章基于电磁感应影响下的Chay神经元模型, 引入了一种以膜电压为阈值的不连续控制策略, 建立了相应的Filippov Chay神经元模型, 探究了在阈值控制策略影响下的神经元放电节律转迁及相应的边界运动. 首先, 对系统的边界动力学及滑膜动力学进行了理论分析. 其次, 利用单双参数分岔图探究了系统多样的放电模式. 再次, 结合Matcont仿真及稳定性理论详细分析了系统的平衡点及其稳定性, 并且利用快慢动力学分析法进一步研究了在阈值影响下所产生的滑膜动力学及各种边界运动的切换. 最后, 通过电突触耦合, 对不同阈值条件下耦合神经元的同步问题进行了讨论. 数值仿真结果表明, 在阈值的调控下Filippov Chay系统会产生滑膜放电活动及相应的穿越运动和擦边运动, 同时其放电周期数也会随着阈值呈现出不同的变化规律, 且对于不同阈值下的电耦合情况而言, 在系统实现完全同步后都会稳定在周期数较低的放电态. 以上所得结果有助于更好地理解神经元滑膜的相关控制, 对进一步探究生物神经系统中复杂放电活动和信息处理的动力学行为提供了一定的帮助.

     

    Abstract: The continuous pumping and transmission of charged ions inside and outside the cell produces the electromagnetic induction effect which in turn affects the electrical activities and pattern switching of neurons and exhibits more abundant discharge characteristics. In this paper, based on the Chay neuron model under the influence of electromagnetic induction, a discontinuous control strategy with membrane voltage as the threshold is introduced, and the corresponding Filippov Chay neuron model is established to explore the neuron firing rhythm transitions and corresponding boundary motions under the influence of the threshold control strategy. Firstly, the boundary dynamics and sliding dynamics of the system are theoretically analyzed. Secondly, the diverse firing patterns of the system are explored using the single and two-parameter bifurcation diagrams. Thirdly, the equilibrium points of the system and their stability are investigated in detail by combining the Matcont simulation and stability theory. The sliding dynamics and the switching of various boundary motions generated under the influence of threshold are further explored by using the fast-slow dynamics analysis. Finally, the synchronization of coupled neurons under different thresholds is discussed by means of electrical synaptic coupling. Numerical simulation results show that the Filippov Chay system will produce sliding firing activities as well as corresponding traversing motion and grazing motion under the regulation of the threshold value. Besides, the number of firing cycles will also show different variation rules with the threshold value. For the cases of electrical synaptic coupling at different thresholds, the system will be stabilized in the firing state with a lower number of cycles after the system realizes the complete synchronization. The above results can contribute to a better understanding of the relevant control associated with neuronal sliding membrane as well as provide a certain help for further investigating the dynamical behavior of complex firing activities and information processing in biological nervous systems.

     

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