Global stability analysis of impulsive BAM type Cohen–Grossberg neural networks with delays

Yang, Fang; Zhang, Chaolong; Wu, Dongqing

doi:10.1016/j.amc.2006.08.016

Cited by 45 publications

(25 citation statements)

References 11 publications

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“…Therefore, it is necessary to consider both the impulsive effect and delay effect when investigating the stability of neural networks [27]. So far, several interesting results have been reported that focusing on the impulsive effect on delayed neural networks, see [27][28][29][30][31][32][33][34][35][36][37][38][39] and references therein. To the best of our knowledge, few authors have considered the dynamical behaviors of the impulsive Cohen-Grossberg neural network model with both time-varying and distributed delays.…”

Section: Introductionmentioning

confidence: 99%

Global Stability of Cohen-Grossberg Neural Networks with Distributed Delays

Zhao

Zhang

2006

Neural Information Processing

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In this paper, the problem of stability analysis for a class of impulsive Cohen-Grossberg neural networks with mixed time delays is considered. The mixed time delays comprise both the time-varying and distributed delays. By employing a combination of the M -matrix theory and analytic methods, several sufficient conditions are obtained to ensure the global exponential stability of equilibrium point for the addressed impulsive Cohen-Grossberg neural network with mixed delays. The proposed method, which does not make use of the Lyapunov functional, is shown to be simple yet effective for analyzing the stability of impulsive neural networks with variable and/or distributed delays. Moreover, the exponential convergence rate is estimated, which depends on the system parameters. The results obtained generalize a few previously known results by removing some restrictions or assumptions. An example with simulation is given to show the effectiveness of the obtained results.

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Section: Introductionmentioning

confidence: 99%

Global Stability of Cohen-Grossberg Neural Networks with Distributed Delays

Zhao

Zhang

2006

Neural Information Processing

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“…C o h e n-G r o s s b e r g neural network [6] and its various generalizations with or without transmission delays and impulsive state displacements have been the subject of intense investigation recently [2], [4], [5], [12], [14], [15]. In a Cohen--Grossberg neural network model, the feedback terms consist of amplification and stabilizing functions which are generally nonlinear.…”

Section: Introductionmentioning

confidence: 99%

Impulsive Cohen-Grossberg neural networks with s-type distributed delays

Akça

Covachev

2011

Tatra Mountains Mathematical Publications

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ABSTRACT. We study impulsive Cohen-Grossberg neural networks with S-type distributed delays. This type of delays in the presence of impulses is more general than the usual types of delays studied in the literature. Using analysis techniques we prove the existence of a unique equilibrium point. By means of simple and efficient Lyapunov functions we present some sufficient conditions for the exponential stability of the equilibrium.

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“…Impulses can make unstable systems stable, so they have been widely used in many fields such as physics, chemistry, biology, population dynamics, and industrial robotics. Some results for impulsive neural networks have been given, for example, see [13][14][15][16][17][18][19][20][21][22] and references therein.…”

Section: Introductionmentioning

confidence: 99%

“…Cao 15 stability analysis of impulsive BAM neural networks with constant delays, time-varying or distributed delays. It may be difficult to apply the Lyapunov approach in [18,21,20] to discuss the exponential stability of model (4.32) and model (2.1).…”

mentioning

confidence: 99%

“…In [18,21], the globally exponential stability for impulsive BAM neural networks with constant delays was investigated by constructing a suitable Lyapunov functional. In [20], authors have considered the impulsive BAM neural networks with distributed delays, several sufficient criteria checking the globally exponential stability were obtained by constructing a suitable Lyapunov functional.…”

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confidence: 99%

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Exponential Stability for Impulsive BAM Neural Networks with Time-Varying Delays and Reaction-Diffusion Terms

Song¹,

Cao²

2007

Adv. Differ Equ.

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Impulsive bidirectional associative memory neural network model with time-varying delays and reaction-diffusion terms is considered. Several sufficient conditions ensuring the existence, uniqueness, and global exponential stability of equilibrium point for the addressed neural network are derived by M-matrix theory, analytic methods, and inequality techniques. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The obtained results in this paper are less restrictive than previously known criteria. Two examples are given to show the effectiveness of the obtained results.

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Global stability analysis of impulsive BAM type Cohen–Grossberg neural networks with delays

Cited by 45 publications

References 11 publications

Global Stability of Cohen-Grossberg Neural Networks with Distributed Delays

Global Stability of Cohen-Grossberg Neural Networks with Distributed Delays

Impulsive Cohen-Grossberg neural networks with s-type distributed delays

Exponential Stability for Impulsive BAM Neural Networks with Time-Varying Delays and Reaction-Diffusion Terms

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