Cellular Neural Networks: Spatially Dependent Templates, Patterns, and Chaos

• Main Authors: Yeh, Li-Chun, 葉俐君
• Other Authors: Juang, J.
• Format: Others
• Language: en_US
• Published: 1998
• Online Access: http://ndltd.ncl.edu.tw/handle/43567984988734806355

碩士 === 國立交通大學 === 應用數學研究所 === 86 === We consider a Cellular Neural Network (CNN) with a bias term z in the integer lattice Z2 on the plane R2 in this thesis. The coupling between cells is "weakly" spatially-dependent. Such coupling is motivated by filling the plane with honeycomb type of lattice. We use two parameters, a and ε to describe the weights between such interacting cells. Like spatially independent template, for fixed ε≠0, we can still partition the parameter space (z,a;ε) into [m,n]ε regions. This, in turn, addresses the so-called "Learning Problem" in CNNs. In the case of complexity of the mosaic pattern, we find that when minimum of m,n is no less than 2, the [m,n] mosaic patterns have spatial chaos. In the temporal chaos part, we mainly consider a Cellular Neural Network with 1-dimension, 3-cell, and z=0. In the spatially independent case with boundary various conditions, such as Direhiet, Neumann, and Periodic boundary condition, we show that the system have no chaotic behavior in the Shil'nikov sense. In addition, we give one example of spatially dependent system that has chaotic behavior in the Shil'nikov sense.