周期刺激下时滞耦合神经振子集群的相位同步

发布时间：2018-02-21 04:30

本文关键词： 神经振子集群周期刺激时滞耦合平均数密度相位同步　出处：《合肥工业大学》2017年硕士论文　论文类型：学位论文

【摘要】：神经系统由大量的神经元集群构成,实验证明神经系统的同步放电行为与神经信息传递和处理密切相关。在神经系统中,过度的同步或不同步均会导致神经疾病发生。突触间隙的存在以及神经信息的有限传播速度会导致时滞的产生。真实的神经系统不可避免地会受到外部周期刺激和噪声的影响。因此,研究周期刺激、噪声和时滞等因素对耦合神经元集群同步动力学行为的影响是理解神经系统信息处理的关键。本文提出了周期刺激作用下时滞耦合神经振子集群的相位模型,引入平均数密度描述神经振子集群的整体活动,利用时滞FPK方程导出了平均数密度的演化方程。1、研究了周期刺激和噪声对神经元集群同步活动的影响,结果表明:刺激对神经振子群同步活动的影响取决于刺激强度和刺激频率。当刺激频率比系统特征频率小很多或者大得多时,神经振子集群的数密度呈现出减幅振荡行为;当刺激频率接近系统特征频率时,神经振子集群趋于完全同步。在相同的刺激频率条件下,刺激越强神经振子集群的同步程度越高。同时噪声强度的增大会抑制神经振子集群的振荡性同步活动。2、研究周期刺激作用下时滞耦合神经振子集群的放电模式。首先分析了无刺激作用下神经元集群的同步活动,结果表明:在时滞的作用下,神经振子集群的数密度表现为幅值逐渐增大的同步振荡,且时滞越大,同步程度越大。其次进一步考虑了周期刺激作用下时滞耦合神经振子集群的放电模式,结果发现:当刺激频率比系统特征频率小很多时,刺激强度的变化可以改变神经元集群的同步放电模式,且弱刺激条件下时滞能增强集群的同步程度,强刺激条件下时滞不影响集群的放电行为。当刺激频率接近系统特征频率时,弱刺激条件下,神经振子集群的同步活动仅由刺激强度主导;强刺激条件下,神经振子集群的同步活动由刺激强度和时滞同时主导。
[Abstract]:The nervous system consists of a large number of neuronal clusters. Experiments show that the synchronous discharge behavior of the nervous system is closely related to the transmission and processing of neural information. Excessive synchronization or non-synchronization can lead to neuropathies. The existence of synaptic spaces and the limited speed of transmission of neural information lead to delays. The real nervous system is inevitably stimulated by external cycles. And the effects of noise. The key to understand the information processing of neural system is to study the effects of periodic stimulation, noise and delay on the synchronous dynamic behavior of coupled neuron clusters. In this paper, a phase model of coupled neural oscillator clusters with time delay under periodic stimulation is proposed. The average density is introduced to describe the global activities of neural oscillator clusters. The evolution equation of mean density is derived by using the time-delay FPK equation. The effects of periodic stimulation and noise on the synchronous activities of neuronal clusters are studied. The results show that the effect of stimulation on the synchronous activity of the neural oscillator group depends on the intensity and frequency of the stimulus. When the stimulus frequency is much smaller or larger than the characteristic frequency of the system, the number density of the neural oscillator cluster exhibits a reduced amplitude oscillation behavior. When the stimulus frequency is close to the characteristic frequency of the system, the neural oscillator cluster tends to be fully synchronized. The stronger the stimulation, the higher the synchronization degree of the neural oscillator cluster, and the higher the noise intensity is, the more the oscillatory synchronous activity of the neural oscillator cluster is inhibited. The discharge mode of the time-delay coupled neural oscillator cluster under periodic stimulation is studied. First of all, we analyze the synchronous activities of neuron clusters without stimulation. The results show that the number density of the neural oscillator cluster is a synchronous oscillation with increasing amplitude under the action of time delay, and the longer the delay is, the greater the time delay is. Secondly, the discharge mode of the time-delay coupled neural oscillator cluster under periodic stimulation is further considered. The results show that when the stimulus frequency is much smaller than the characteristic frequency of the system, The change of stimulus intensity can change the synchronous discharge pattern of the neuron cluster, and the delay can enhance the synchronization degree of the cluster under the condition of weak stimulation. When the stimulus frequency is close to the characteristic frequency of the system, when the stimulus frequency is close to the characteristic frequency of the system, the synchronous activity of the neural oscillator cluster is dominated only by the intensity of the stimulus under the weak stimulus condition, while under the strong stimulus condition, the synchronous activity of the neural oscillator cluster is dominated by the intensity of the stimulus. The synchronous activity of neural oscillator clusters is dominated by both stimulus intensity and time delay.
【学位授予单位】：合肥工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O242.1;R338

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