MODELLING REACTION-DIFFUSION PARTIAL Differential EQUATION USING THE CELLULAR NEURAL NETWORK Universal MACHINE

摘要

The main object of the following paper is to show that physical implementations of the Cellular Neural network Universal Machine (CNN UM) paradigm can appear a useful tool for modeling Reaction-Diffusion Partial Differential Equations (PDEs). The main advantage offered by the proposed way of modeling is a Processing speed (network's inherent parallelism), which outperforms capabilities of computer-based approaches while its main drawback are inaccurate computations (typical for analog implementations). Three main issues were Presented in the paper. The former one concerns modeling of linear Reaction--Diffusion Partial Differential Equations using Cellular Neural Network Universal Machine. An appropriate procedure which is required for implementing equations of this type has been discussed along With its application for Laplace equation solving. The second problem which has been discussed concerns implementation of systems of equations in the considered Structure. A method which allows for solving systems of Reaction-Diffusion PDEs within a framework Of CNN UM was proposal. The method is based on appropriate organization of data which are to be handled in a network and does not require any modifications, neither of CNN UM architecture, nor of its Processing element's structure. The proposed method can be considered also as a means for implementing two-layer Cellular Neural Networks into a CNN UM Paradigm framework.