本文關(guān)鍵詞： 神經(jīng)振子集群 周期刺激 時(shí)滯耦合 平均數(shù)密度 相位同步　出處：《合肥工業(yè)大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：神經(jīng)系統(tǒng)由大量的神經(jīng)元集群構(gòu)成,實(shí)驗(yàn)證明神經(jīng)系統(tǒng)的同步放電行為與神經(jīng)信息傳遞和處理密切相關(guān)。在神經(jīng)系統(tǒng)中,過度的同步或不同步均會導(dǎo)致神經(jīng)疾病發(fā)生。突觸間隙的存在以及神經(jīng)信息的有限傳播速度會導(dǎo)致時(shí)滯的產(chǎn)生。真實(shí)的神經(jīng)系統(tǒng)不可避免地會受到外部周期刺激和噪聲的影響。因此,研究周期刺激、噪聲和時(shí)滯等因素對耦合神經(jīng)元集群同步動(dòng)力學(xué)行為的影響是理解神經(jīng)系統(tǒng)信息處理的關(guān)鍵。本文提出了周期刺激作用下時(shí)滯耦合神經(jīng)振子集群的相位模型,引入平均數(shù)密度描述神經(jīng)振子集群的整體活動(dòng),利用時(shí)滯FPK方程導(dǎo)出了平均數(shù)密度的演化方程。1、研究了周期刺激和噪聲對神經(jīng)元集群同步活動(dòng)的影響,結(jié)果表明:刺激對神經(jīng)振子群同步活動(dòng)的影響取決于刺激強(qiáng)度和刺激頻率。當(dāng)刺激頻率比系統(tǒng)特征頻率小很多或者大得多時(shí),神經(jīng)振子集群的數(shù)密度呈現(xiàn)出減幅振蕩行為;當(dāng)刺激頻率接近系統(tǒng)特征頻率時(shí),神經(jīng)振子集群趨于完全同步。在相同的刺激頻率條件下,刺激越強(qiáng)神經(jīng)振子集群的同步程度越高。同時(shí)噪聲強(qiáng)度的增大會抑制神經(jīng)振子集群的振蕩性同步活動(dòng)。2、研究周期刺激作用下時(shí)滯耦合神經(jīng)振子集群的放電模式。首先分析了無刺激作用下神經(jīng)元集群的同步活動(dòng),結(jié)果表明:在時(shí)滯的作用下,神經(jīng)振子集群的數(shù)密度表現(xiàn)為幅值逐漸增大的同步振蕩,且時(shí)滯越大,同步程度越大。其次進(jìn)一步考慮了周期刺激作用下時(shí)滯耦合神經(jīng)振子集群的放電模式,結(jié)果發(fā)現(xiàn):當(dāng)刺激頻率比系統(tǒng)特征頻率小很多時(shí),刺激強(qiáng)度的變化可以改變神經(jīng)元集群的同步放電模式,且弱刺激條件下時(shí)滯能增強(qiáng)集群的同步程度,強(qiáng)刺激條件下時(shí)滯不影響集群的放電行為。當(dāng)刺激頻率接近系統(tǒng)特征頻率時(shí),弱刺激條件下,神經(jīng)振子集群的同步活動(dòng)僅由刺激強(qiáng)度主導(dǎo);強(qiáng)刺激條件下,神經(jīng)振子集群的同步活動(dòng)由刺激強(qiáng)度和時(shí)滯同時(shí)主導(dǎo)。
[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.
【學(xué)位授予單位】：合肥工業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O242.1;R338

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