Global stability analysis of Cohen–Grossberg neural networks with time varying delays

Arik, Sabri; Orman, Zeynep

doi:10.1016/j.physleta.2005.04.095

Cited by 156 publications

(69 citation statements)

References 16 publications

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“…for t > 0, i = 1, 2, · · · , n. Furthermore, model (3) also comprises the following Cohen-Grossberg neural network model with neither impulses nor stochastic effects [13] (4) is also a general neural network that covers the delayed Cohen-Grossberg neural network models studied in [3][4][5][6][7][8][9][10][11][12].…”

Section: Model Description and Preliminariesmentioning

confidence: 99%

“…In practice, due to the finite speeds of the switching and transmission of signals, time delays do exist in a working network and thus should be incorporated into the model equation [3,26,27]. In recent years, the dynamical behaviors of Cohen-Grossberg neural networks with constant delays or time-varying delays or distributed delays have been studied, see for example [3][4][5][6][7][8][9][10][11][12][13] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

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Stability analysis of impulsive stochastic Cohen–Grossberg neural networks with mixed time delays

Song

Wang

2008

Physica A: Statistical Mechanics and its Applications

149

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In this paper, the problem of stability analysis for a class of impulsive stochastic Cohen-Grossberg neural networks with mixed delays is considered. The mixed time delays comprise both the time-varying and infinite distributed delays. By employing a combination of the M -matrix theory and stochastic analysis technique, a sufficient condition is obtained to ensure the existence, uniqueness, and exponential p-stability of the equilibrium point for the addressed impulsive stochastic 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 or stochastic neural networks with variable and/or distributed delays. We then extend our main results to the case where the parameters contain interval uncertainties. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. An example is given to show the effectiveness of the obtained results.

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Section: Model Description and Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stability analysis of impulsive stochastic Cohen–Grossberg neural networks with mixed time delays

Song

Wang

2008

Physica A: Statistical Mechanics and its Applications

149

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“…It is also important to incorporate time delay in various neural networks. In recent years, there exist some results on global asymptotical stability, global exponential stability and periodic solutions for the neural networks with constant delays or time-varying delays (see, e.g., [1]- [6], [8], [10]- [17], [19]- [24], [29]- [31]). Although the use of finite delays in models with delayed feedback provides a good approximation to simple circuits consisting of a small number of neurons, neural networks usually should have a spatial extent due to the presence of a multitude of parallel pathways with a variety of axon sizes and lengths.…”

Section: Introductionmentioning

confidence: 99%

Existence and stability of periodic solutions for Cohen–Grossberg neural networks with multiple delays

2004

Chaos, Solitons & Fractals

100

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In this paper, a generalized model of Cohen-Grossberg neural networks with periodic coefficients and both time-varying and distributed delays is investigated. By employing Mawhin's continuation theorem, analytic methods, inequality technique and M -matrix theory, some sufficient conditions ensuring the existence, uniqueness and global exponential stability of the periodic oscillatory solution for Cohen-Grossberg neural networks with both time-varying and distributed delays are obtained. Two examples are given to show the effectiveness of the obtained results.

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“…In addition, assumption (H3) on the behaved functions in our results is the same as that in [5,8,18], and the condition for differentiability imposed on behaved functions in [2][3][4], [6], [7], [9][10][11] is removed in our results. Remark 4.…”

Section: Remarkmentioning

confidence: 91%

“…For simplicity of the presentation, the proof is skipped. In [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], [19,20,21,23,25,26], the amplification functions were required to satisfy 0 ( )…”

Section: Remarkmentioning

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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Global stability analysis of Cohen–Grossberg neural networks with time varying delays

Cited by 156 publications

References 16 publications

Stability analysis of impulsive stochastic Cohen–Grossberg neural networks with mixed time delays

Stability analysis of impulsive stochastic Cohen–Grossberg neural networks with mixed time delays

Existence and stability of periodic solutions for Cohen–Grossberg neural networks with multiple delays

Global Stability of Cohen-Grossberg Neural Networks with Distributed Delays

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