In this paper, the Cohen-Grossberg neural networks with time-varying delays and impulses are considered. New sufficient conditions for the existence and global exponential stability of a unique equilibrium point are e...In this paper, the Cohen-Grossberg neural networks with time-varying delays and impulses are considered. New sufficient conditions for the existence and global exponential stability of a unique equilibrium point are established by using the fixed point theorem and Lyapunov functional. An example is given to demonstrate the effectiveness of our results.展开更多
In this paper,we study the anti-periodic solutions for a class of impulsive Cohen-Grossberg neural networks with mixed delays.By using analysis techniques,some sufficient conditions are obtained which guarantee the ex...In this paper,we study the anti-periodic solutions for a class of impulsive Cohen-Grossberg neural networks with mixed delays.By using analysis techniques,some sufficient conditions are obtained which guarantee the existence and global exponential stability of the anti-periodic solutions.The criteria extend and improve some earlier results.Moreover,we give an examples to illustrate our main results.展开更多
Purpose–The purpose of this paper is to develop a methodology for the existence and global exponential stability of the unique equilibrium point of a class of impulsive Cohen-Grossberg neural networks.Design/methodol...Purpose–The purpose of this paper is to develop a methodology for the existence and global exponential stability of the unique equilibrium point of a class of impulsive Cohen-Grossberg neural networks.Design/methodology/approach–The authors perform M-matrix theory and homeomorphism mapping principle to investigate a class of impulsive Cohen-Grossberg networks with time-varying delays and distributed delays.The approach builds on new sufficient criterion without strict conditions imposed on self-regulation functions.Findings–The authors’approach results in new sufficient criteria easy to verify but without the usual assumption that the activation functions are bounded and the time-varying delays are differentiable.An example shows the effectiveness and superiority of the obtained results over some previously known results.Originality/value–The novelty of the proposed approach lies in removing the usual assumption that the activation functions are bounded and the time-varying delays are differentiable,and the use of M-matrix theory and homeomorphism mapping principle for the existence and global exponential stability of the unique equilibrium point of a class of impulsive Cohen-Grossberg neural networks.展开更多
We investigate the global exponential stability of Cohen-Grossberg neural networks （CGNNs） with variable moments of impulses using B-equivalence method. Under cer- tain conditions, we show that each solution of the ...We investigate the global exponential stability of Cohen-Grossberg neural networks （CGNNs） with variable moments of impulses using B-equivalence method. Under cer- tain conditions, we show that each solution of the considered system intersects each surface of discontinuity exactly once, and that the variable-time impulsive systems can be reduced to the fixed-time impulsive ones. The obtained results imply that impul- sive CGNN will remain stability property of continuous subsystem even if the impulses are of somewhat destabilizing, and that stabilizing impulses can stabilize the unsta- ble continuous subsystem at its equilibrium points. Moreover, two stability criteria for the considered CGNN by use of proposed comparison system are obtained. Finally, the theoretical results are illustrated by two examples.展开更多
文摘In this paper, the Cohen-Grossberg neural networks with time-varying delays and impulses are considered. New sufficient conditions for the existence and global exponential stability of a unique equilibrium point are established by using the fixed point theorem and Lyapunov functional. An example is given to demonstrate the effectiveness of our results.
基金supported by National Nature Science Foundation under Grant 11161029,Chinascience and technology research projects of guangxi under Grant 2013YB282,201203YB186
文摘In this paper,we study the anti-periodic solutions for a class of impulsive Cohen-Grossberg neural networks with mixed delays.By using analysis techniques,some sufficient conditions are obtained which guarantee the existence and global exponential stability of the anti-periodic solutions.The criteria extend and improve some earlier results.Moreover,we give an examples to illustrate our main results.
基金supported by the National Natural Science Foundation of China under Grants 61074073,61034005,61273022,Program for New Century Excellent Talents in University of China(NCET-10-0306)the Fundamental Research Funds for the Central Universities under Grant N110504001.
文摘Purpose–The purpose of this paper is to develop a methodology for the existence and global exponential stability of the unique equilibrium point of a class of impulsive Cohen-Grossberg neural networks.Design/methodology/approach–The authors perform M-matrix theory and homeomorphism mapping principle to investigate a class of impulsive Cohen-Grossberg networks with time-varying delays and distributed delays.The approach builds on new sufficient criterion without strict conditions imposed on self-regulation functions.Findings–The authors’approach results in new sufficient criteria easy to verify but without the usual assumption that the activation functions are bounded and the time-varying delays are differentiable.An example shows the effectiveness and superiority of the obtained results over some previously known results.Originality/value–The novelty of the proposed approach lies in removing the usual assumption that the activation functions are bounded and the time-varying delays are differentiable,and the use of M-matrix theory and homeomorphism mapping principle for the existence and global exponential stability of the unique equilibrium point of a class of impulsive Cohen-Grossberg neural networks.
文摘We investigate the global exponential stability of Cohen-Grossberg neural networks （CGNNs） with variable moments of impulses using B-equivalence method. Under cer- tain conditions, we show that each solution of the considered system intersects each surface of discontinuity exactly once, and that the variable-time impulsive systems can be reduced to the fixed-time impulsive ones. The obtained results imply that impul- sive CGNN will remain stability property of continuous subsystem even if the impulses are of somewhat destabilizing, and that stabilizing impulses can stabilize the unsta- ble continuous subsystem at its equilibrium points. Moreover, two stability criteria for the considered CGNN by use of proposed comparison system are obtained. Finally, the theoretical results are illustrated by two examples.
