摘要
Pre-Bötzinger复合体是新生哺乳动物呼吸节律起源的关键部位,是呼吸节律产生的中枢.忆阻器的功能类似于神经元突触的可塑性,可用其模拟磁通量.本文在Butera动力学模型的基础上引入刺激电流和磁通控制忆阻器,分别研究这两个因素对单个pre-Bötzinger复合体神经元中混合簇放电模式的影响.通过无量纲化的方法对变量进行时间尺度分析,结果表明,模型包含3个不同的时间尺度.通过快慢分解和分岔分析研究了神经元混合簇放电产生和转迁的动力学机制.电流和磁通量都可以影响混合簇中胞体簇的个数,减小电流和磁通量的值,混合簇中胞体簇的个数也会相应减少,并使簇的类型由“fold/homoclinic”型簇放电转迁为经由“fold/homoclinic”滞后环的“Hopf/Hopf”型簇放电.双参数分岔分析表明,随着钙离子浓度的逐渐增加,全系统轨线在鞍结分岔曲线和同宿轨分岔曲线之间来回跃迁,是混合簇的产生分岔机制.全系统轨线在鞍结分岔曲线和同宿轨分岔曲线之间跃迁的次数,与混合簇中胞体簇的个数相对应.
The pre-Bötzinger complex is essential for the generation of the respiratory rhythm of newborn mammals and it is the center for the generation of the respiratory rhythm.The function of the memristor is similar to the plasticity of neuronal synapses,which can be used to simulate magnetic flux.In this paper,by adding stimulation current and magnetic flux-controlled memristor to the Butera dynamics model,we mainly investigate the influences of these two factors on the mixed bursting firing pattern of a single pre-Bötzinger neuron.Timescale analysis of variables is carried out by dimensionless methods.The results indicate that the model contains three different time scales.The dynamic mechanism of mixed bursting is studied through fast-slow decomposition and bifurcation analysis.Both the stimulation current and the magnetic flux can affect the number of somatic part of mixed bursting.Decrease the values of stimulation currentand magnetic flux,the number of somatic bursts will also decrease accordingly,and the stimulation current and magnetic flux can make the firing patterns of the somatic bursts transit from“fold/homoclinic”bursting to“Hopf/Hopf”bursting via“fold/homoclinic”hysteresis loop.Two-parameter bifurcation analysis in(h,[Ca])plane shows that with the gradual increase of calcium ion,the trajectory of the full system crosses back and forth between the fold bifurcation and homoclinic bifurcation curve,which implies the dynamic mechanism of mixed bursting mainly rely on these two bifurcations.The number of transitions between the fold bifurcation and homoclinic bifurcation curve of the full system trajectory corresponds to the amount of somatic bursts in the mixed bursting.
作者
冀文超
段利霞
齐会如
Ji Wenchao;Duan Lixia;Qi Huiru(Colloge of Science,North China University of Technology,Beijing 100144,China)
出处
《力学学报》
EI
CAS
CSCD
北大核心
2021年第6期1733-1746,共14页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金(11872003)
北方工业大学“特色学科建设”项目(110052972027/014)资助.
