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Global stability of CohenGrossberg neural networks with distributed delays
 in Lecture Notes in Computer Science
, 2006
"... In this paper, the problem of stability analysis for a class of impulsive CohenGrossberg neural networks with mixed time delays is considered. The mixed time delays comprise both the timevarying and distributed delays. By employing a combination of the Mmatrix theory and analytic methods, several ..."
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In this paper, the problem of stability analysis for a class of impulsive CohenGrossberg neural networks with mixed time delays is considered. The mixed time delays comprise both the timevarying and distributed delays. By employing a combination of the Mmatrix theory and analytic methods, several sufficient conditions are obtained to ensure the global exponential stability of equilibrium point for the addressed impulsive CohenGrossberg 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. Key words: CohenGrossberg neural network, global exponential stability, timevarying delays, distributed delays, impulsive effect 1.
Antiperiodic solutions for CohenGrossberg shunting
"... inhibitory neural networks with delays ..."
Delayindependent globally asymptotic stability of Cohen–Grossberg neural networks
 International Journal of Information and Systems Sciences
, 2005
"... Abstract. The dynamic behavior of CohenGrossberg neural networks with multiple delays and nonsymmetric interconnecting structure is investigated. The sufficient conditions for the globally asymptotic stability of equilibrium point are given by way of constructing a suitable Lyapunov functional. Com ..."
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Abstract. The dynamic behavior of CohenGrossberg neural networks with multiple delays and nonsymmetric interconnecting structure is investigated. The sufficient conditions for the globally asymptotic stability of equilibrium point are given by way of constructing a suitable Lyapunov functional. Combined with the linear matrix inequality (LMI) technique and the properties of matrix norm, two practical corollaries are derived. All results are established without assuming the differentiability and monotonicity of activation functions. The simulation samples have proved the effectiveness of the conclusions. Key Words. CohenGrossberg neural networks, multiple delays, Lyapunov functional, and globally asymptotic stability
ftp ejde.math.txstate.edu (login: ftp) EXISTENCE OF NONOSCILLATORY SOLUTIONS TO HIGHERORDER MIXED DIFFERENCE EQUATIONS
"... Abstract. In this paper, we consider the higher order neutral nonlinear difference equation ∆ m (x(n) + p(n)x(τ(n))) + f1(n, x(σ1(n))) − f2(n, x(σ2(n))) = 0, ∆ m (x(n) + p(n)x(τ(n))) + f1(n, x(σ1(n))) − f2(n, x(σ2(n))) = g(n), ∆ m (x(n) + p(n)x(τ(n))) + lX bi(n)x(σi(n)) = 0. i=1 We obtain suffi ..."
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Abstract. In this paper, we consider the higher order neutral nonlinear difference equation ∆ m (x(n) + p(n)x(τ(n))) + f1(n, x(σ1(n))) − f2(n, x(σ2(n))) = 0, ∆ m (x(n) + p(n)x(τ(n))) + f1(n, x(σ1(n))) − f2(n, x(σ2(n))) = g(n), ∆ m (x(n) + p(n)x(τ(n))) + lX bi(n)x(σi(n)) = 0. i=1 We obtain sufficient conditions for the existence of nonoscillatory solutions. Consider the difference equations 1.
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"... Existence and stability of periodic solution in impulsive neural networks with both variable and distributed delays1 ..."
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Existence and stability of periodic solution in impulsive neural networks with both variable and distributed delays1
Exponential Stability of ReactionDiffusion Generalized CohenGrossberg Neural Networks with both Variable and Distributed Delays1
"... In this paper, a generalized reactiondiffusion model of CohenGrossberg neural networks with timevarying and distributed delays is investigated. By employing analytic methods, inequality technique and Mmatrix theory, some sufficient conditions ensuring the existence, uniqueness and global exponen ..."
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In this paper, a generalized reactiondiffusion model of CohenGrossberg neural networks with timevarying and distributed delays is investigated. By employing analytic methods, inequality technique and Mmatrix theory, some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for CohenGrossberg neural networks with timevarying and distributed delays are obtained. Several examples are given to show the effectiveness of the obtained results.
NEW RESULT OF EXISTENCE OF PERIODIC SOLUTION FOR A HOPFIELD NEURAL NETWORKS WITH NEUTRAL TIMEVARYING DELAYS
"... Abstract. In this paper, a Hopfield neural network with neutral timevarying delays is investigated by using the continuation theorem of Mawhin’s coincidence degree theory and some analysis technique. Without assuming the continuous differentiability of timevarying delays, sufficient conditions f ..."
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Abstract. In this paper, a Hopfield neural network with neutral timevarying delays is investigated by using the continuation theorem of Mawhin’s coincidence degree theory and some analysis technique. Without assuming the continuous differentiability of timevarying delays, sufficient conditions for the existence of the periodic solutions are given. The result of this paper is new and extends previous known result. 1
Periodic Solutions Of A ThreeSpecies Food Chain
, 2007
"... A fairly realistic threespecies food chain model based on the LeslieGower scheme is investigated, and some sufficient conditions for the existence of positive periodic solutions of the model are obtained. 1 ..."
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A fairly realistic threespecies food chain model based on the LeslieGower scheme is investigated, and some sufficient conditions for the existence of positive periodic solutions of the model are obtained. 1
Research Article Existence and Exponential Stability of Periodic Solution for a Class of Generalized Neural Networks with Arbitrary Delays
, 2009
"... By the continuation theorem of coincidence degree and Mmatrix theory, we obtain some sufficient conditions for the existence and exponential stability of periodic solutions for a class of generalized neural networks with arbitrary delays, which are milder and less restrictive than those of previous ..."
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By the continuation theorem of coincidence degree and Mmatrix theory, we obtain some sufficient conditions for the existence and exponential stability of periodic solutions for a class of generalized neural networks with arbitrary delays, which are milder and less restrictive than those of previous known criteria. Moreover our results generalize and improve many existing ones. Copyright q 2009 Yimin Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1.