标题: 两个耦合双细胞类神经网路的动态系统
Dynamics in coupled two two-cell Cellular Neural Network systems
作者: 刘玟毅
Wen-Yi Liu
林松山
Song-Sun Lin
应用数学系所
关键字: 细胞类神经网路;混沌;Lyapunov 指数;Cellular Neural Networks;CNN;chaos;lady's shoe;Lyapunov exponent
公开日期: 2004
摘要: 在本篇论文中,我们研究具有四个细胞之类神经网路模型的混沌行为,此模型可以视为两个双细胞类神经网路的组合,而且这两个类神经网路之间是有交互影响的;如果我们只考虑其中一个类神经网路的话,这与Zou & Nossek[19]以及杨定挥的博士论文[22]的情况是不一样的,他们所考虑的模型是一个有平滑输入函数的非自主性(non-autonomous)系统,而我们的模型是以片段型线性函数作为输入函数的自主性(autonomous)系统,此输入函数是跟细胞本身以及输出函数有关系的。在某些参数范围,我们找到形如高跟鞋的混沌吸引子(chaotic attractor)。为了研究四个细胞之类神经网路的分歧和混沌现象,我们使用快速傅利叶转换(Fast Fourier Transform)与计算Lyapunov指数(Lyapunov exponent)等数值方法。此外,我们也发展出一套用来计算Lyapunov指数的演算法,而且这个演算法是同时适用于自主性与非自主性的系统。
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.
URI: http://140.113.39.130/cdrfb3/record/nctu/#GT009222507
http://hdl.handle.net/11536/76301
显示于类别:Thesis


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