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. In this article, we present a lattice differential equation model for a class of neural networks. We define a subset of the equilibrium solutions we call mosaic equilibrium solutions. Existence and stability theorems are proved for mosaic equilibrium solutions. Regions of stability are defined and spatial entropy calculations, as a measure of the complexity of the system, are presented that give insights in to the effects of spatial coupling. 1. Introduction. Neural networks are computational models characterized by patterns of weighted interconnections between neurons or cells. The method of determining the weights is called a training algorithm which resets the weights in accordance with some activation function. The result is a system which trains itself to recognize patterns or emulate functions. Traditional nets such as the Hopfield Net and the standard Backpropagation Neural Network have been intriguing to many disciplines. Although training can be slow, the resulting network ...

constructed using particle swarm optimisation for spatio-temporal evolutionary pattern identification. International Journal of Bifurcation and Chaos, 18 (12). pp.