In this paper, the authors analyze the stability of a kind of discrete-time Hopfield neural network with asymptotical weighted matrix, which can be expressed as the product of a positive definite diagonal matrix and a...In this paper, the authors analyze the stability of a kind of discrete-time Hopfield neural network with asymptotical weighted matrix, which can be expressed as the product of a positive definite diagonal matrix and a symmetric matrix. We obtain that it has asymptotically stable equilibriums if the network is updated asynchronously, and asymptotically stable equilibriums or vibrating final stage with 2 period if updated synchronously. To prove these, Lassale＇s invariance principle in difference equation is applied.展开更多
文摘In this paper, the authors analyze the stability of a kind of discrete-time Hopfield neural network with asymptotical weighted matrix, which can be expressed as the product of a positive definite diagonal matrix and a symmetric matrix. We obtain that it has asymptotically stable equilibriums if the network is updated asynchronously, and asymptotically stable equilibriums or vibrating final stage with 2 period if updated synchronously. To prove these, Lassale＇s invariance principle in difference equation is applied.
