兩個耦合雙細胞類神經網路的動態系統

Abstract

在本篇論文中，我們研究具有四個細胞之類神經網路模型的混沌行為，此模型可以視為兩個雙細胞類神經網路的組合，而且這兩個類神經網路之間是有交互影響的；如果我們只考慮其中一個類神經網路的話，這與Zou & Nossek[19]以及楊定揮的博士論文[22]的情況是不一樣的，他們所考慮的模型是一個有平滑輸入函數的非自主性﹙non-autonomous﹚系統，而我們的模型是以片段型線性函數作為輸入函數的自主性﹙autonomous﹚系統，此輸入函數是跟細胞本身以及輸出函數有關係的。在某些參數範圍，我們找到形如高跟鞋的混沌吸引子﹙chaotic attractor﹚。為了研究四個細胞之類神經網路的分歧和混沌現象，我們使用快速傅利葉轉換﹙Fast Fourier Transform﹚與計算Lyapunov指數﹙Lyapunov exponent﹚等數值方法。此外，我們也發展出一套用來計算Lyapunov指數的演算法，而且這個演算法是同時適用於自主性與非自主性的系統。

In this thesis we study the chaotic behavior of four-neuron cellular neural networks model, this model can be treated as the combination of two two-neuron cellular neural networks and there are interactions between these two neural networks. If we only consider one of them, this is different from the case in ZN-case\cite{Zou1} and T.H.Yang's Ph.D Thesis\cite{Lin4}. The model they considered is a non-autonomous system with smooth input function. The one we consider is an autonomous system with piecewise-linear input which is related to neuron itself and output function. In some parameters ranges, we find a ladyshoe-like chaotic attractor. The numerical methods employed are of Fast Fourier Transform and Lyapunov exponents to study the bifurcation and chaotic phenomena of four-neuron neural network. Furthermore, an algorithm for computing Lyapunov exponents which is both adapted for autonomous and non-autonomous system is developed.