發(fā)布時間：2018-05-14 07:17

  本文選題：Morris-Lecar模型 + 簇放電　； 參考：《華南理工大學(xué)》2015年碩士論文

【摘要】：隨著計算神經(jīng)科學(xué)的不斷發(fā)展與完善,各類神經(jīng)元模型的放電模式及分支理論已經(jīng)被廣泛研究,如Hodgkin-Huxley模型、Morris-Lecar模型、Hindmarsh-Rose模型等,為我們更加深入的學(xué)習(xí)和研究神經(jīng)系統(tǒng)的信息編碼和認(rèn)知功能奠定了基礎(chǔ).本文主要研究改進的Morris-Lecar模型及建立在脊髓第I層神經(jīng)元上的一類Morris-Lecar-like模型的動力學(xué)性質(zhì),得到的主要結(jié)果如下:對于改進的Morris-Lecar模型,我們首先通過數(shù)值模擬研究生理參數(shù)膜電容對神經(jīng)元膜電位發(fā)放序列的影響,得到豐富的神經(jīng)元放電模式.然后結(jié)合峰峰間期序列ISIs分岔圖我們發(fā)現(xiàn),當(dāng)膜電容對應(yīng)不同的值時,一定范圍內(nèi)時間尺度因子和鈣離子最大電導(dǎo)的變化所引起的神經(jīng)元的放電模式有很大的區(qū)別,如峰發(fā)放、簇發(fā)放或不規(guī)則發(fā)放,并且在這些發(fā)放模式之間的轉(zhuǎn)移中我們也發(fā)現(xiàn)了幾種典型的非線性動力學(xué)現(xiàn)象,包括倍周期分岔、加周期分岔等現(xiàn)象,使我們進一步理解了神經(jīng)元的信息編碼與膜電容、離子通道等共同作用之間的關(guān)系.文章最后研究Morris-Lecar-like模型,我們首先對雙參數(shù)分支圖中的Bogdanov-Takens點附近的分支情況進行數(shù)值計算,得到相應(yīng)的鞍-結(jié)點分支曲線、Hopf分支曲線和同宿軌分支曲線;同時為了使神經(jīng)元產(chǎn)生更豐富的放電現(xiàn)象,我們引進慢變量,根據(jù)快子系統(tǒng)的平衡點曲線上支的Hopf分支點數(shù)量的不同,我們對得到的五種簇放電模式的動力學(xué)性質(zhì)進行了研究.
[Abstract]:With the development and perfection of computational neuroscience, the discharge modes and branching theories of various neuronal models, such as the Hodgkin-Huxley model, the Morris-Lecar model and Hindmarsh-Rose model, have been extensively studied. It lays a foundation for us to further study the information coding and cognitive function of the nervous system. In this paper, the dynamic properties of the improved Morris-Lecar model and a class of Morris-Lecar-like model based on the spinal layer I neurons are studied. The main results are as follows: for the improved Morris-Lecar model, Firstly, the effects of membrane capacitance on the release sequence of membrane potential of neurons were studied by numerical simulation, and a rich pattern of neuronal discharge was obtained. Then combining with the ISIs bifurcation diagram of the interpeak series, we find that when the membrane capacitance corresponds to different values, the firing patterns of neurons caused by the change of the time scale factor and the maximum conductance of calcium ion in a certain range are quite different, such as peak discharge. Cluster distribution or irregular distribution, and in the transfer between these modes, we also find several typical nonlinear dynamic phenomena, including double period bifurcation, plus period bifurcation and so on. We can further understand the relationship between the information coding of neurons and the interaction of membrane capacitance and ion channel. Finally, we study the Morris-Lecar-like model. Firstly, we numerically calculate the bifurcation near the Bogdanov-Takens point in the two-parameter bifurcation graph, and obtain the corresponding saddle-node bifurcation curve and homoclinic orbit bifurcation curve. At the same time, in order to make neurons produce more abundant discharge phenomena, we introduce slow variables. According to the number of Hopf branch points on the equilibrium point curve of fast subsystem, we study the dynamic properties of the five cluster discharge modes.
【學(xué)位授予單位】：華南理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O175

【參考文獻】

相關(guān)碩士學(xué)位論文 前3條

1 汪雷;神經(jīng)元與神經(jīng)元回路的模型分析[D];華南理工大學(xué);2011年

2 李敏;兩類生物模型的分支研究[D];華南理工大學(xué);2013年

3 孫丹華;CA1&CA3錐體神經(jīng)元模型的動力學(xué)分析[D];華南理工大學(xué);2014年

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本文編號：1886883