Impulses-induced exponential stability in recurrent delayed neural networks

Neurocomputing

Volumn 74, Issue 17, 2011, Pages 3204-3211

  Wu, Quanjun ^a,b   Zhou, Jin ^b   Xiang, Lan ^b  

^a SHANGHAI UNIVERSITY OF ELECTRIC POWER   (China)

^b SHANGHAI UNIVERSITY   (China)

Author keywords

Chaotic delayed neural network; Global exponential stability; Impulsive coupled neurons; Recurrent delayed neural network; Time varying delay

Indexed keywords

DELAYED NEURAL NETWORKS; DIFFERENTIAL INEQUALITIES; DISTINCTIVE FEATURES; GLOBAL EXPONENTIAL STABILITY; IMPULSIVE COUPLED NEURONS; NEURONAL CONNECTIVITY; TIME-VARYING DELAY;

DYNAMICAL SYSTEMS; ROBUSTNESS (CONTROL SYSTEMS); STABILITY CRITERIA; TIME VARYING CONTROL SYSTEMS; TIME VARYING NETWORKS;

RECURRENT NEURAL NETWORKS;

ARTICLE; ARTIFICIAL NEURAL NETWORK; GLOBAL EXPONENTIAL STABILITY; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; MATHEMATICAL PHENOMENA; NERVE CELL; PRIORITY JOURNAL; SIMULATION;

EID: 80052925863     PISSN: 09252312     EISSN: 18728286     Source Type: Journal    
DOI: 10.1016/j.neucom.2011.05.001     Document Type: Article

References (32)

1. Hale J.K. Theory of Functional Differential Equations 1977, Springer-Verlag, New York.
2. Cohen M.A., Grossberg S. Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Transactions on Systems, Man, and Cybernetics, SMC 1983, 13(5):815-826.
3. Hopfield J.J. Neurons with graded response have collective computational properties like those of two-state neurons. Proceedings of the National Academy of Science, USA (Biophysics) 1984, 81:3088-3092.
4. Arik S. An analysis of global asymptotic stability of delayed cellular neural networks. IEEE Transactions on Neural Networks 2002, 13(5):1239-1242.
5. Cao J.D., Wang J. Global asymptotic stability of a general class of recurrent neural networks with time-varying delays. IEEE Transactions on Circuits and Systems I-Regular Papers 2003, 50(1):34-44.
6. He Y., Wu M., She J.H. An improved global asymptotic stability criterion for delayed cellular neural networks. IEEE Transactions on Neural Networks 2006, 17(1):250-252.
7. Wang Z., Liu Y., Li M., Liu X. Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Transactions on Neural Networks 2006, 17(3):814-820.
8. Huang H., Ho D.W.C., Qu Y.Z. Robust stability of stochastic delayed additive neural networks with Markovian switching. Neural Networks 2007, 20(7):799-809.
9. Guan Z.H., Chen G.R. On delayed impulsive Hopfield neural networks. Neural Networks 1999, 12(2):273-280.
10. Chen T.P. Global exponential stability of delayed Hopfield neural networks. Neural Networks 2001, 14(8):977-980.
11. Liao X.F., Chen G.R., Sanchez E.N. Delay-dependent exponential stability analysis of delayed neural networks: an LMI approach. Neural Networks 2002, 15(7):855-866.
12. Mohamad S., Gopalsamy K. Exponential stability of continuous-time and discrete-time cellular neural networks with delays. Applied Mathematics and Computation 2003, 135(1):17-38.
13. Yang Z.C., Xu D.Y. Stability analysis of delay neural networks with impulsive effects. IEEE Transactions on Circuits and Systems II-Express Briefs 2005, 52(8):517-521.
14. Yang Z.C., Xu D.Y. Stability analysis of delay neural networks with impulsive effects. Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis 2006, 13:563-573.
15. Chen Z., Ruan J. Global stability analysis of impulsive Cohen-Grossberg neural networks with delay. Physics Letters A 2005, 345:101-111.
16. Song Q.K., Cao J.D. Impulsive effects on stability of fuzzy Cohen-Grossberg neural networks with time-varying delays. IEEE Transactions on Systems, Man and Cybernetics-Part B: Cybernetics 2007, 37(3):733-741.
17. Zeng Z.G., Wang J. Global exponential stability of recurrent neural networks with time-varying delays in the presence of strong external stimuli. Neural Networks 2006, 19(10):1528-1537.
18. Ho D.W.C., Liang J.L., Lam J. Global exponential stability of impulsive high-order BAM neural networks with time-varying delays. Neural Networks 2006, 19(10):1581-1590.
19. Gopalsamy K., Sariyasa Time delays and stimulus-dependent pattern formation in periodic environments in isolated neurons. IEEE Transactions on Neural Networks 2002, 13(3):551-563.
20. Lu Q.S., Gu H.G., Yang Z.Q., Shi X., Duan L.X., Zheng Y.H. Dynamics of firing patterns, synchronization and resonances in neuronal electrical activities: experiments and analysis. Acta Mechanica Sinica 2008, 24:593-628.
21. Wang Z.D., Liu Y.R., Liu X.H. State estimation for jumping recurrent neural networks with discrete and distributed delays. Neural Networks 2009, 22(1):41-48.
22. Chen G.R., Zhou J., Liu Z.R. Global synchronization of coupled delayed neural networks and applications to chaotic CNN models. International Journal of Bifurcation and Chaos 2004, 14(7):2229-2240.
23. Zhou J., Liu Z.R., Chen G.R. Dynamics of periodic delayed neural networks. Neural Networks 2004, 17(1):87-101.
24. Guan Z.H., Lam J., Chen G.R. On impulsive autoassociative neural networks. Neural Networks 2000, 13(1):63-69.
25. Yang T. Impulsive Systems and Control: Theory and Applications 2001, Nova Science, Huntington, NY.
26. Li C.D., Liao X.F., Yang X.F. Impulsive stabilization and synchronization of a class of chaotic delay systems. Chaos 2005, 15(4):043103.
27. Wu Q.J., Zhou J., Xiang L., Liu Z.R. Impulsive control and synchronization of chaotic Hindmarsh-Rose models for neuronal activity. Chaos, Solitons and Fractals 2009, 41(5):2706-2715.
28. Dong M., Zhang H.G., Wang Y.C. Dynamics analysis of impulsive stochastic Cohen-Grossberg neural networks with Markovian jumping and mixed time delays. Neurocomputing 2009, 72(7-9):1999-2004.
29. Gu H.B., Jiang H.J., Teng Z.D. BAM-type impulsive neural networks with time-varying delays. Nonlinear Analysis: Real World Application 2009, 10(5):3059-3072.
30. Hindmarsh J.L., Rose R.M. A mode of neuronal bursting using three coupled first order differential equations. Proceedings of the Royal Society of London. Series B, Biological Sciences 1984, 221(1222):87-102.
31. Zhou J., Wu Q.J. Exponential stability of impulsive delayed linear differential equations. IEEE Transactions on Circuits and Systems II-Express Briefs 2009, 56(9):744-748.
32. Zhou J., Xiang L., Liu Z.R. Synchronization in complex delayed dynamical networks with impulsive effects. Physica A 2007, 384(2):684-692.