In this paper, we investigate the dynamics in a class of discrete-time neuron mod-els. The neuron model we discussed, defined by such periodic input-output mapping as a sinusoidal function, has a remarkably larger mem...In this paper, we investigate the dynamics in a class of discrete-time neuron mod-els. The neuron model we discussed, defined by such periodic input-output mapping as a sinusoidal function, has a remarkably larger memory capacity than the conven-tional association system with the monotonous function. Our results show that the orbit of the model takes a conventional bifurcation route, from stable equilibrium, to periodicity, even to chaotic region. And the theoretical analysis is verified by numerical simula...展开更多
The aim of this paper is to provide a sys- tematic review on the framework to analyze dynamics in recurrently connected neural networks with discontinu- ous right-hand sides with a focus on the authors＇ works in the ...The aim of this paper is to provide a sys- tematic review on the framework to analyze dynamics in recurrently connected neural networks with discontinu- ous right-hand sides with a focus on the authors＇ works in the past three years. The concept of the Filippov so- lution is employed to define the solution of the neural network systems by transforming them to differential in- clusions. The theory of viability provides a tool to study the existence and uniqueness of the solution and the Lya- punov function （functional） approach is used to investi- gate the global stability and synchronization. More pre- cisely, we prove that the diagonal-dominant conditions guarantee the existence, uniqueness, and stability of a general class of integro-differential equations with （al- most） periodic self-inhibitions, interconnection weights, inputs, and delays. This model is rather general and in- cludes the well-known Hopfield neural networks, Cohen- Grossberg neural networks, and cellular neural networks as special cases. We extend the absolute stability anal- ysis of gradient-like neural network model by relaxing the analytic constraints so that they can be employed to solve optimization problem with non-smooth cost func- tions. Furthermore, we study the global synchronization problem of a class of linearly coupled neural network with discontinuous right-hand sides.展开更多
基金Specialized research fund for outstanding young scholars in universities of Shanghai (GrantNo2-2008-26)
文摘In this paper, we investigate the dynamics in a class of discrete-time neuron mod-els. The neuron model we discussed, defined by such periodic input-output mapping as a sinusoidal function, has a remarkably larger memory capacity than the conven-tional association system with the monotonous function. Our results show that the orbit of the model takes a conventional bifurcation route, from stable equilibrium, to periodicity, even to chaotic region. And the theoretical analysis is verified by numerical simula...
文摘The aim of this paper is to provide a sys- tematic review on the framework to analyze dynamics in recurrently connected neural networks with discontinu- ous right-hand sides with a focus on the authors＇ works in the past three years. The concept of the Filippov so- lution is employed to define the solution of the neural network systems by transforming them to differential in- clusions. The theory of viability provides a tool to study the existence and uniqueness of the solution and the Lya- punov function （functional） approach is used to investi- gate the global stability and synchronization. More pre- cisely, we prove that the diagonal-dominant conditions guarantee the existence, uniqueness, and stability of a general class of integro-differential equations with （al- most） periodic self-inhibitions, interconnection weights, inputs, and delays. This model is rather general and in- cludes the well-known Hopfield neural networks, Cohen- Grossberg neural networks, and cellular neural networks as special cases. We extend the absolute stability anal- ysis of gradient-like neural network model by relaxing the analytic constraints so that they can be employed to solve optimization problem with non-smooth cost func- tions. Furthermore, we study the global synchronization problem of a class of linearly coupled neural network with discontinuous right-hand sides.
