A global stable analysis for CGNN and CNN with asymmetric weights

We consider the CGNN model of neural networks (Cohen and Grossberg, 1983) and cellular neural network (CNN) model (Yang and Chua, 1988) with asymmetric weights. Using Lasalle´s invariance principle, we proved that if the weight matrix in CGNN can be decomposed as the product of a symmetric matrix and a positively definite diagonal matrix, then all bounded orbits of the above model converge to equilibriums (as t→+∞). By piecelinear stable analysis we discussed the stability of CNN with asymmetric weights and the weight design for image thinning.