【摘要】：生物神經(jīng)元系統(tǒng)是由數(shù)目巨大的神經(jīng)細(xì)胞組成,這些神經(jīng)細(xì)胞之間通過放電進(jìn)行著豐富的信息傳遞活動(dòng),構(gòu)成了生物神經(jīng)元的信息網(wǎng)絡(luò)支持生物體的正常生命活動(dòng)。神經(jīng)元細(xì)胞之間傳遞信息是通過峰峰放電形式實(shí)現(xiàn)的,不同放電方式編碼了不同的信息,因此可以通過研究神經(jīng)元系統(tǒng)峰峰放電探索神經(jīng)元放電規(guī)律和動(dòng)力學(xué)特性。同步在自然界中無處不在,在神經(jīng)元系統(tǒng)中兩個(gè)神經(jīng)元細(xì)胞之間放電同步對(duì)于神經(jīng)系統(tǒng)的記憶、信息平衡和記憶等具有重要的意義。兩個(gè)神經(jīng)細(xì)胞之間的同步放電是整個(gè)神經(jīng)網(wǎng)絡(luò)的基礎(chǔ),所以兩個(gè)神經(jīng)細(xì)胞之間的耦合神經(jīng)元系統(tǒng)同步是整個(gè)神經(jīng)網(wǎng)絡(luò)信息傳遞的關(guān)鍵。本文做了如下幾方面研究:(1)基于單個(gè)神經(jīng)元系統(tǒng)通過化學(xué)突觸耦合方式得到耦合神經(jīng)元系統(tǒng),從單個(gè)神經(jīng)元系統(tǒng)的穩(wěn)定性出發(fā)判斷了耦合神經(jīng)元系統(tǒng)的穩(wěn)定性、霍普分岔。改變系統(tǒng)一個(gè)參數(shù)研究了耦合系統(tǒng)在單參數(shù)變化下動(dòng)力學(xué)特性,得到神經(jīng)元系統(tǒng)中存在倍化分岔、加周期分岔和混沌等豐富的動(dòng)力學(xué)特性。(2)給出了系統(tǒng)雙參數(shù)平面分岔圖。通過同時(shí)改變系統(tǒng)中兩個(gè)系統(tǒng)參數(shù),用不同顏色代表不同的放電周期清晰的顯示了在某個(gè)特定的取值區(qū)域耦合系統(tǒng)的放電特性,可以為醫(yī)學(xué)實(shí)驗(yàn)研究神經(jīng)元編碼方式提供理論依據(jù)。離散第三個(gè)參數(shù)觀察雙參數(shù)分岔的變化趨勢(shì),實(shí)現(xiàn)了通過多參數(shù)研究耦合神經(jīng)元?jiǎng)恿W(xué)特性。(3)從耦合神經(jīng)元的耦合強(qiáng)度出發(fā)研究神經(jīng)元的同步。首先在理論上獲取了實(shí)現(xiàn)系統(tǒng)同步時(shí)耦合強(qiáng)度與系統(tǒng)參數(shù)之間的關(guān)系,在理論推導(dǎo)中運(yùn)用了穩(wěn)定等價(jià)和李雅普諾夫函數(shù)相關(guān)理論。在較弱的耦合強(qiáng)度下耦合神經(jīng)元系統(tǒng)很難實(shí)現(xiàn)完全同步,在較強(qiáng)的耦合強(qiáng)度下則容易實(shí)現(xiàn)完全同步。接著研究系統(tǒng)參數(shù)和耦合強(qiáng)度共同作用下耦合系統(tǒng)的同步情況,給出了系統(tǒng)參數(shù)和耦合強(qiáng)度共同影響下耦合系統(tǒng)能否實(shí)現(xiàn)同步的同步圖,得到每一個(gè)系統(tǒng)參數(shù)對(duì)耦合系統(tǒng)同步的影響。(4)考慮了時(shí)滯和噪聲因素對(duì)耦合系統(tǒng)同步的影響。在耦合系統(tǒng)中分別加入了時(shí)滯和噪聲的因素,通過數(shù)值模擬可以發(fā)現(xiàn)適當(dāng)?shù)臅r(shí)滯和外界噪聲有利于耦合神經(jīng)元系統(tǒng)達(dá)到同步,促進(jìn)神經(jīng)網(wǎng)絡(luò)的信息傳遞,但是給出的時(shí)滯和耦合強(qiáng)度共同作用耦合系統(tǒng)同步圖揭示時(shí)滯和噪聲破壞系統(tǒng)的同步。(5)最后給出了在不同的耦合強(qiáng)度下耦合子系統(tǒng)的放電周期情況,對(duì)比兩個(gè)子系統(tǒng)在相同耦合強(qiáng)度下的放電情況,揭示了耦合強(qiáng)度對(duì)耦合系統(tǒng)影響的方式。本論文研究可以全面的揭示耦合神經(jīng)元系統(tǒng)在多參數(shù)影響的動(dòng)力學(xué)性質(zhì)和不同參數(shù)影響下的耦合神經(jīng)元同步,可以得到如何實(shí)現(xiàn)耦合系統(tǒng)達(dá)到同步促進(jìn)神經(jīng)網(wǎng)絡(luò)的信息傳遞。研究結(jié)果可以為醫(yī)學(xué)生理實(shí)驗(yàn)和人工智能提供理論依據(jù)。
[Abstract]:The biological neuron system is composed of a large number of nerve cells. These nerve cells carry out abundant information transmission activities through the discharge, which constitute the information network of the biological neurons to support the normal life activities of the organism. The transmission of information between neuronal cells is realized by peak discharge, and different discharge modes encode different information. Therefore, we can explore the law and dynamic characteristics of neuronal discharge by studying the peak discharge of neuron system. Synchronization is ubiquitous in nature. In neuron system, the synchronization of discharge between two neuronal cells is of great significance to the memory, information balance and memory of the nervous system. The synchronous discharge between two nerve cells is the basis of the whole neural network, so the synchronization of the coupled neuron system between the two nerve cells is the key to the information transmission of the whole neural network. In this paper, the following studies have been done: (1) based on the chemical synaptic coupling of a single neuron system, the stability of the coupled neuron system is judged from the stability of a single neuron system, and the Hoppe bifurcation is obtained. By changing one parameter of the system, the dynamical characteristics of the coupled system with single parameter variation are studied, and the rich dynamical characteristics of the neuron system such as doubling bifurcation, periodic bifurcation and chaos are obtained. (2) the two-parameter plane bifurcation diagram of the system is given. By changing the two system parameters at the same time, the discharge characteristics of the coupled system in a particular value area are clearly displayed by different colors representing different discharge cycles. It can provide theoretical basis for the study of neural coding mode in medical experiments. The discrete third parameter observed the variation trend of two-parameter bifurcation and realized the study of coupling neuron dynamics through multi-parameter. (3) the synchronization of neurons was studied from the coupling strength of coupling neurons. Firstly, the relationship between the coupling strength and the system parameters is obtained theoretically, and the theory of stability equivalence and Lyapunov function is used in the theoretical derivation. It is difficult to achieve complete synchronization in the coupled neuron system under the weak coupling strength, but it is easy to achieve complete synchronization under the strong coupling strength. Then the synchronization of the coupled system under the joint action of the system parameters and the coupling strength is studied, and the synchronization diagram of whether the coupling system can achieve synchronization under the influence of the system parameters and the coupling strength is given. The effects of each system parameter on the synchronization of coupled systems are obtained. (4) the effects of delay and noise on the synchronization of coupled systems are considered. The factors of delay and noise are added to the coupled system respectively. Through numerical simulation, it can be found that the appropriate time delay and external noise are favorable to the synchronization of the coupled neuron system and the information transmission of the neural network can be promoted. However, the synchronization diagram of the coupled system with time-delay and coupling strength is given to reveal the synchronization between the time-delay and the noise failure system. (5) finally, the discharge period of the coupled subsystem under different coupling strengths is given. By comparing the discharge of the two subsystems under the same coupling strength, the influence of coupling strength on the coupling system is revealed. In this paper, the dynamic properties of coupled neuron system under the influence of multiple parameters and the coupling neuron synchronization under different parameters can be fully revealed, and how to achieve synchronization of coupled system to promote the information transmission of neural network can be obtained. The results can provide theoretical basis for medical physiological experiments and artificial intelligence.
【學(xué)位授予單位】：蘭州交通大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：Q42;O175

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