The existence, uniqueness and global asymptotic stability for the equilibrium of Hopfield-type neural networks with diffusion effects are studied. When the activation functions are monotonously nondecreasing, differen...The existence, uniqueness and global asymptotic stability for the equilibrium of Hopfield-type neural networks with diffusion effects are studied. When the activation functions are monotonously nondecreasing, differentiable, and the interconnected matrix is related to the Lyapunov diagonal stable matrix, the sufficient conditions guaranteeing the existence of the equilibrium of the system are obtained by applying the topological degree theory. By means of constructing the suitable average Lyapunov functions, the global asymptotic stability of the equilibrium of the system is also investigated. It is shown that the equilibrium （if it exists） is globally asymptotically stable and this implies that the equilibrium of the system is unique.展开更多
The Hopfield-type continuous neural networks with global exponential stability are veryessential for the real-time solution for the various kinds of optimization problems,such asthe A/D converter design problem.From a...The Hopfield-type continuous neural networks with global exponential stability are veryessential for the real-time solution for the various kinds of optimization problems,such asthe A/D converter design problem.From a mathematical viewpoint this means that thenetwork should have a unique equilibrium point that is globally and exponentially stable.展开更多
基金Project supported by the National Natural Science Foundation of China (No.10571078)the Natural Science Foundation of Gansu Province of China (No.3ZX062-B25-012)
文摘The existence, uniqueness and global asymptotic stability for the equilibrium of Hopfield-type neural networks with diffusion effects are studied. When the activation functions are monotonously nondecreasing, differentiable, and the interconnected matrix is related to the Lyapunov diagonal stable matrix, the sufficient conditions guaranteeing the existence of the equilibrium of the system are obtained by applying the topological degree theory. By means of constructing the suitable average Lyapunov functions, the global asymptotic stability of the equilibrium of the system is also investigated. It is shown that the equilibrium （if it exists） is globally asymptotically stable and this implies that the equilibrium of the system is unique.
基金Project supported by the National Natural Science Foundation of Chinathe National Climb Project.
文摘The Hopfield-type continuous neural networks with global exponential stability are veryessential for the real-time solution for the various kinds of optimization problems,such asthe A/D converter design problem.From a mathematical viewpoint this means that thenetwork should have a unique equilibrium point that is globally and exponentially stable.
基金The Science Foundation for Youths of Shanxi Province(2010JQ1016)the National Natural Science Foundation of China(10926152)the Science Research Foundation of Department of Education of Shaanxi Province(9JK613)
