細胞類神經網路:馬賽克花樣，分歧點與複雜性

Abstract

我們主要探討一個細胞類神經網路模型的馬賽克花樣，在這裡考慮的輸出函數在無窮遠的地方並不是平坦的。許多複雜的參數區域是可以被完整地描繪出來，每一個參數區域的熵是可以藉由轉換矩陣的方法算出來﹔我們也利用參數 和 來討論一些馬賽克花樣的分歧現象，在這裡 是一個偏壓項、 是和鄰近細胞的互動比重。特別地，對於一個小的互動比重 ，我們發現當加入偏壓項之後，許多新的複雜參數區域都會產生。然而當 增加到某一個範圍之後，許多上述的複雜參數區域會消失，但是又有一些新的複雜參數範圍會產生。

We study mosaic patterns of a one-dimensional Cellular Neural Network with an output function which is non-flat at infinity. Spatial chaotic regions are completely characterized. Moreover, each of their exact corresponding entropy is obtained via the method of transition matrices. We also study the bifurcation phenomenon of mosaic patterns with bifurcation parameters z and β. Here z is a source (or bias) term and β is the interaction weight between the neighboring cells. In particular, we find that by injecting the source term, i.e.z≠0, a lot of new chaotic patterns emerge with a smaller interaction weight β. However, as β increases to a certain range, most of previously observed chaotic patterns disappear, while other new chaotic patterns emerge.