Equivalence and stability of two-layered cellular neural network solving saint venant ID equation

Cellular Neural Network (CNN) has been used for solving Partial Differential Equations (PDE). However, the equivalence and stability of system should be considered carefully in a particular problem. In this paper, we introduce the model CNN for solving set of two PDEs describing water flow channels (called Saint Venant equation). We analyze the approximation and topological equivalence issues between Cellular Partial Difference Differential Equation (CPDDE) and its original PDEs. The stability of CNN system is also proved from discovering the equilibrium of the state and output of each cell. The paper has 4 parts. After introduction, part 2 gives a two-layered CNN 1D model for solving PDE Saint Venant equation. In the part 3 the equivalence and stability of the CNN model are proved, then simulation using FPGA. The conclusions are given in the last part.