網路中的動力學在生活和自然界中扮演重要的角色，例如神經系統中神經細胞彼此互相連結和影響所構成的複雜網路。本論文將介紹兩個方法，如何藉由量測網路中節點的動力學行為得到網路結構的資訊。第一個是scaling of noisy fluctuation，可以得知節點的相對連結數；第二個是Granger causality的分析，可以得知兩個節點間有無因果相關。我們先利用可激發的FitzHugh-Nagumo model(FHN)模型去模仿神經系統在網路中的行為，用以上兩個方法來分析網路中每個節點的時間序列，比較分析出來的網路結構和實際模擬所設定的網路結構之間的關係。最後再將此兩種分析的方法應用在實驗的數據，包括心臟的培養和神經的培養隨著時間其網路結構的變化，以及神經的培養在經過藥物Bicuculline(BMI)和Glutamate的影響網路結構的改變。其中Bicuculline用來破壞其神經傳導的抑制神經衝動機制，而Glutamate為神經細胞間傳遞神經衝動訊息的化學物質。The dynamics in a network is important in nature, for example the dynamics in complex neural network. The neural cells are coupled by the connection of the network. There are two methods in my thesis to obtain the network information from time-series data of its nodes. The first is the method of scaling of noisy fluctuation. The second is the Granger causality analysis. In the first method, we get information on the relative node degree in the network. By Granger causality analysis, we get the causal relation between the nodes in the network. We implement these two method and tested using networks of coupled excitable FitzHugh-Nagumo (FHN) elements to mimic excitable networks.We then apply this method to analyse the data from two experiments. One is the Multi-Electrode-Arrays (MEA) experimental data which record the time-series data in cultured neurons in vitro. We want to study the change of network with time and two kinds of drags, the Bicuculline (BMI) and Glutamate. Bicuculline inhibit the inhibition of the mechanism of neuron, and Glutamate is neural transmitter. The other is the video image data which record the time series data in developing cardiac culture in vitro. Then we discussed the cell-cell interactions in these neural and cardiac cultures.
