In this paper,by applying Lasalle's in variance principle and some results about the trace of a matrix,we propose a method for estimating the topological structure of a discrete dynamical network based on the dyna...In this paper,by applying Lasalle's in variance principle and some results about the trace of a matrix,we propose a method for estimating the topological structure of a discrete dynamical network based on the dynamicalevolution of the network.The network concerned can be directed or undirected,weighted or unweighted,and the localdynamics of each node can be nonidentical.The connections among the nodes can be all unknown or partially known.Finally,two examples,including a Henon map and a central network,are illustrated to verify the theoretical results.展开更多
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
基金Supported by the Foundation of Jiangsu Polytechnic University under Grant No.JS200805National Natural Science Foundation of China under Grant No.10672146Shanghai Leading Academic Discipline Project under Grant No.S30104
文摘In this paper,by applying Lasalle's in variance principle and some results about the trace of a matrix,we propose a method for estimating the topological structure of a discrete dynamical network based on the dynamicalevolution of the network.The network concerned can be directed or undirected,weighted or unweighted,and the localdynamics of each node can be nonidentical.The connections among the nodes can be all unknown or partially known.Finally,two examples,including a Henon map and a central network,are illustrated to verify the theoretical results.
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.
