Multi-layer Cellular Neural Networks: Theory and Applications to Modeling Nitric Oxide Diffusion in Nervous Systems

In this paper, we study the dynamic range of multi-layer cellular neural networks (CNN’s) by using Lyapunov functions. A theorem is presented to guarantee the existence of equilibrium point of multi-layer CNN. A theorem on globally stable equilibrium point of multi-layer CNN is given. Multi-layer CNN’s are used to model some functions of nitric oxide (NO) in nervous systems. In a 2-layer CNN model, the first CNN layer implements synaptic events such as image processing tasks. During these synaptic events artificial NO sources are triggered by the outputs of the first CNN layer. In the 2nd CNN layer, a NO diffusion model is implemented. The output of the 2nd CNN layer functions as a feedback, which mimics the actions of NO to synaptic events, to the first CNN layer. This kind of feedback from the 2nd CNN layer introduces “plasticity” into the CNN synaptic law of the first CNN layer. We improve the NO diffusion model in the 2nd CNN layer by introducing the third CNN layer, which feedbacks the output of the first CNN layer to the NO diffusion model in the second CNN layer. As an application of CNN NO model, we use it to improve the performance of edge detection CNN. Copyright c ©2002 Yang’s Scientific Research Institute, LLC. All rights reserved.