具有时滞的抑制性自突触诱发的神经放电的加周期分岔  

Period-adding bifurcation of neural firings induced by inhibitory autapses with time-delay

作　　者：丁学利[1] 李玉叶[2] 

机构地区：[1]阜阳职业技术学院基础教学部,阜阳236031 [2]赤峰学院数学与统计学院,赤峰024000

出　　处：《物理学报》2016年第21期67-77,共11页Acta Physica Sinica

基　　金：国家自然科学基金青年科学基金(批准号:11402039);安徽省自然科学基金一般项目(批准号:KJ2015B008)资助的课题~~

摘　　要：神经放电节律在神经系统功能实现中起着重要的作用.具有自突触(起始和结束于同一细胞的突触)的神经元普遍存在于神经系统,本文研究了单神经元模型在抑制性自突触作用下的放电节律.结果发现,随着时滞和/或耦合强度的增加,可以诱发Rulkov神经元模型放电节律的加周期分岔.随着放电节律的周期数的增加,平均放电频率增大,当时滞和/或耦合强度大于某一阈值时,频率大于没有自突触时的放电频率.用快慢变量分离方法可以获得没有自突触的神经放电节律的分岔结构,可用于认识外界负向脉冲诱发的新节律.这些新的节律模式与加周期分岔中的节律模式一致.研究结果不仅揭示了抑制性自突触可以诱发典型的非线性现象——加周期分岔,还给出了抑制性自突触可以提高放电频率的新现象,与以前的自突触压制放电的观点不同,进一步丰富了对抑制性自突触诱发的非线性现象的认识.Neural firing rhythm plays an important role in achieving the function of a nervous system. Neurons with autapse,which starts and ends in the same cell, are widespread in the nervous system. Previous results of both experimental and theoretical studies have shown that autaptic connection plays a role in influencing dynamics of neural firing patterns and has a significant physiological function. In the present study, the dynamics of a neuronal model, i.e., Rulkov model with inhibitory autapse and time delay, is investigated, and compared with the dynamics of neurons without autapse.The bifurcations with respect to time-delay and the coupling strength are extensively studied, and the time series of membrane potentials is also calculated to confirm the bifurcation analysis. It can be found that with the increase of time-delay and/or the coupling strength, the period-adding bifurcation of neural firing patterns can be induced in the Rulkov neuron model. With the increase of the period number of the firing rhythm, the average firing frequency increases.When time-delay and/or coupling strength are/is greater than their/its corresponding certain thresholds/threshold, the average firing frequency is higher than that of the neuron without autapse. Furthermore, new bursting patterns, which appear at suitable time delays and coupling strengths, can be well interpreted with the dynamic responses of an isolated single neuron to a negative square current whose action time, duration, and strength are similar to those of the inhibitory coupling current modulated by the coupling strength and time delay. The bursts of neurons with autapse show the same pattern as the square negative current-induced burst of the isolated single neuron when the time delay corresponds to the phase. The bifurcation structure of the neural firing rhythm of the neuron without autapse can be obtained with the fast-slow dissection method. The dynamic responses of the isolated bursting neuron to the negative square current are acquired by using the fast-sl

关 键 词：加周期分岔 神经放电 抑制性自突触 时滞 

分 类 号：Q42[生物学—神经生物学]