哺乳动物皮层神经元模型的放电模式研究-《中国医学物理学杂志》

文章信息/Info

Author(s):: CHENG Yuanfen; LIU Shenquan; School of Mathematics, South China University of Technology, Guangzhou 510640, China

Keywords:: Keywords: neuron model; bifurcation; first Lyapunov coefficient; fast-slow dynamics; electric coupling

摘要:: 针对一类三维哺乳动物新皮层神经元模型进行分析。该模型是结合Wilson模型和Hindmarsh-Rose模型而建立的，得到的快变量遵守欧姆定律。快慢动力学对时间尺度相差很大的系统的分析是非常有效的，因此本研究使用快慢动力学方法，并结合理论计算和数值模拟来探究该模型的动力学行为。首先，随着系统控制参数的改变，发现了3类簇放电模式；然后，计算一阶Lyapunov系数，以此确定Hopf分岔是超临界或次临界的；最后，将模型与经典的Morris-Lecar模型耦合，分析并讨论了耦合强度及外界交流刺激对耦合系统的影响。

Abstract:: Abstract: A three-dimensional neuron model which express the characteristics of mammals new cortex is analyzed in this study. The neuron model is obtained by combining Wilson model and Hindmarsh-Rose model, and its fast variables obey Ohm’s law. The fast-slow dynamical methods is effective for systematic analysis with large differences in time scales. Hence the fast-slow dynamics method is adopted and combined with theoretical calculation and numerical simulation to explore the dynamic activity of the model. As the control parameters change, 3 types of bursting patterns are demonstrated. Furthermore, the first Lyapunov coefficient of the Hopf bifurcation is calculated, thereby determining whether the Hopf bifurcation is subcritical or supercritical. Finally, the model is coupled with the classic Morris-Lecar model for analyzing and discussing the effects of coupling strength and external alternating current stimulation on the coupled system.