Global exponential stability of Cohen–Grossberg neural networks with variable delays

Zhang, Jiye; Suda, Yoshihiro; Komine, Hisanao

doi:10.1016/j.physleta.2005.02.005

Cited by 84 publications

(29 citation statements)

References 21 publications

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“…The Cohen-Grossberg neural networks, initially proposed and studied in [1], have attracted increasing interest due to their potential applications. Such applications depend heavily on their dynamical properties, the most important being the stability of neural dynamical systems [2][3][4].…”

Section: Introductionmentioning

confidence: 99%

Global Attractivity of Almost Periodic Sequence Solutions of Delayed Discrete-Time Neural Networks

2011

Arab J Sci Eng

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Section: Introductionmentioning

confidence: 99%

Global Attractivity of Almost Periodic Sequence Solutions of Delayed Discrete-Time Neural Networks

2011

Arab J Sci Eng

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“…It follows from the property of M-matrix [17] that the Theorem 2 in [10] can be obtained by Corollary 4.…”

Section: Corollarymentioning

confidence: 93%

“…[4][5][6][7][8][9][10][11][12][13][14]). The purpose of this paper is to study the following generalized Cohen-Grossberg neural networks with variable delays:…”

Section: §1 Introductionmentioning

confidence: 99%

Global exponential stability of Cohen-Grossberg neural networks with variable delays

Zhang

Shi

2009

Appl. Math. J. Chin. Univ.

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A class of generalized Cohen-Grossberg neural networks(CGNNs) with variable delays are investigated. By introducing a new type of Lyapunov functional and applying the homeomorphism theory and inequality technique, some new conditions are derived ensuring the existence and uniqueness of the equilibrium point and its global exponential stability for CGNNs. These results obtained are independent of delays, develop the existent outcome in the earlier literature and are very easily checked in practice. §1 IntroductionCohen and Grossberg [1] proposed a class of neural networks in 1983, which can be described by the following ordinary differential equations:where n denotes the number of neurons in the network, x i (t) denotes the state of the ith neuron and the activation function f j (·) denotes the output of the jth neuron at time t, the n × n connection matrix W = (w ij ) represents the neuron interconnections. Model (1) includes a large number of models from neurobiology and population biology [2] . In particular, it includes the popular Hopfield neural networks [3] and BSB models. Moreover, this type of neural networks has been widely studied due to its potential applications in many areas such as associative memory and optimization. Because of the finite switching speeds of neurons and amplifiers, time delays inevitably exist in biological and artificial neural networks. Therefore, Cohen-Grossberg neural networks with time delays have been widely studied, which is described asReceived: 2008-03-23 MR Subject Classification: 34K20, 92B20, 37N25, 93C23

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“…To the best of our knowledge, few authors have considered the global exponential stability of the Cohen-Grossberg neural networks with time-varying delays and impulses. In this paper, we use the method in [9][10] and focus on the global exponential stability of the Cohen-Grossberg neural networks with time-varying delays and impulses. By applying the fixed point theorem and Lyapunov functional, we obtain some new criteria for the global exponential stability of the Cohen-Grossberg neural networks with time-varying delays and impulses.…”

Section: Introductionmentioning

confidence: 99%

Global exponential stability of Cohen-Grossberg neural networks with time-varying delays and impulses

Zhu

Fang

Zhang

2009

J. Shanghai Univ.(Engl. Ed.)

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Global exponential stability of Cohen–Grossberg neural networks with variable delays

Cited by 84 publications

References 21 publications

Global Attractivity of Almost Periodic Sequence Solutions of Delayed Discrete-Time Neural Networks

Global Attractivity of Almost Periodic Sequence Solutions of Delayed Discrete-Time Neural Networks

Global exponential stability of Cohen-Grossberg neural networks with variable delays

Global exponential stability of Cohen-Grossberg neural networks with time-varying delays and impulses

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