Exponential stability of artificial neural networks with distributed delays and large impulses

Mohamad, Sannay; Gopalsamy, K.; Akça, Haydar

doi:10.1016/j.nonrwa.2007.01.011

Cited by 106 publications

(42 citation statements)

References 20 publications

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“…Throughout this paper, we always assume that the impulsive jumps P k and Q k satisfy (referring to [28][29][30][31][32][33][34][35][36][37])…”

Section: Kij(s)gj(yj(t − S))dsmentioning

confidence: 99%

“…Many interesting results on impulsive effect have been gained, e.g., Refs. [28][29][30][31][32][33][34][35][36][37]. As artificial electronic systems, neural networks such as CNNs, bidirectional neural networks and recurrent neural networks often are subject to impulsive perturbations, which can affect dynamical behaviors of the systems just as time delays.…”

Section: Introductionmentioning

confidence: 99%

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Integro-differential inequality and stability of BAM FCNNs with time delays in the leakage terms and distributed delays

Zhang

2011

J Inequal Appl

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In this paper, a class of impulsive bidirectional associative memory (BAM) fuzzy cellular neural networks (FCNNs) with time delays in the leakage terms and distributed delays is formulated and investigated. By establishing an integro-differential inequality with impulsive initial conditions and employing M-matrix theory, some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive BAM FCNNs with time delays in the leakage terms and distributed delays are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on the delay kernel functions and system parameters. It is believed that these results are significant and useful for the design and applications of BAM FCNNs. An example is given to show the effectiveness of the results obtained here.

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“…Throughout this paper, we always assume that the impulsive jumps P k and Q k satisfy (referring to [28][29][30][31][32][33][34][35][36][37])…”

Section: Kij(s)gj(yj(t − S))dsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Integro-differential inequality and stability of BAM FCNNs with time delays in the leakage terms and distributed delays

Zhang

2011

J Inequal Appl

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“…The literature is very rich of works on the asymptotic behavior of solutions for special cases of system (1) (see for instance [10][11][12][13][14][15][16][17][18][19]). Here the integral terms represent some kind of distributed delays but discrete delays may be recovered as well by considering delta Dirac distributions.…”

Section: Introductionmentioning

confidence: 99%

Long Time Behavior for a System of Differential Equations with Non-Lipschitzian Nonlinearities

Tatar

2014

Advances in Artificial Neural Systems

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We consider a general system of nonlinear ordinary differential equations of first order. The nonlinearities involve distributed delays in addition to the states. In turn, the distributed delays involve nonlinear functions of the different variables and states. An explicit bound for solutions is obtained under some rather reasonable conditions. Several special cases of this system may be found in neural network theory. As a direct application of our result it is shown how to obtain global existence and, more importantly, convergence to zero at an exponential rate in a certain norm. All these nonlinearities (including the activation functions) may be non-Lipschitz and unbounded.

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“…Using matrix theory and constructing a Liapunov function, he proves the existence, uniqueness and global asymptotic stability of the equilibrium point of (4). Recent work has extended the Lyapunov function/functional approach to study stability in networks with time varying delays [28,40], networks with impulses [33] and with stochastic perturbations [42,44]. The Lyapunov functional approach has also been used to formulate linear matrix inequality (LMI) conditions for stability [35].…”

Section: Introductionmentioning

confidence: 99%

Approximating the stability region of a neural network with a general distribution of delays

Jessop

Campbell

2010

Neural Networks

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We investigate the linear stability of a neural network with distributed delay, where the neurons are identical. We examine the stability of a symmetrical equilibrium point via the analysis of the characteristic equation both when the connection matrix is symmetric and when it is not. We determine a mean delay and distribution independent stability region. We then illustrate a way of improving on this conservative result by approximating the true region of stability when the actual distribution is not known, but some moments or cumulants of the distribution are. Finally, we compare the approximate stability regions with the stability regions in the case of the uniform and gamma distributions. We show that the approximations improve as more moments or cumulants are used, and that the approximations using cumulants give better results than the ones using moments.

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Exponential stability of artificial neural networks with distributed delays and large impulses

Cited by 106 publications

References 20 publications

Integro-differential inequality and stability of BAM FCNNs with time delays in the leakage terms and distributed delays

Integro-differential inequality and stability of BAM FCNNs with time delays in the leakage terms and distributed delays

Long Time Behavior for a System of Differential Equations with Non-Lipschitzian Nonlinearities

Approximating the stability region of a neural network with a general distribution of delays

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