Global asymptotic stability to a generalized Cohen-Grossberg BAM neural networks of neutral type delays

Neural Networks

Volumn 25, Issue , 2012, Pages 94-105

  Zhang, Zhengqiu ^a   Liu, Wenbin ^a   Zhou, Dongming ^b  

^a HUNAN UNIVERSITY   (China)

^b YUNNAN UNIVERSITY   (China)

Author keywords

Generalized Cohen Grossberg BAM neural networks of neutral type; Global asymptotic stability; Homeomorphism theory; Inequality technique; Lyapunov functional; The existence and uniqueness of an equilibrium point

Indexed keywords

EXISTENCE AND UNIQUENESS; GLOBAL ASYMPTOTIC STABILITY; HOMEOMORPHISM THEORY; INEQUALITY TECHNIQUES; LYAPUNOV FUNCTIONALS; NEUTRAL TYPE;

ASYMPTOTIC STABILITY; LYAPUNOV FUNCTIONS;

NEURAL NETWORKS;

ARTICLE; ARTIFICIAL NEURAL NETWORK; BRAIN FUNCTION; COHEN GROSSBERG BAM NEURAL NETWORK; INFORMATION PROCESSING; LINEAR SYSTEM; MATHEMATICAL COMPUTING; NEUROTRANSMISSION; PRIORITY JOURNAL; STATISTICAL ANALYSIS; SYSTEMS THEORY; VALIDITY;

NEURAL NETWORKS (COMPUTER); REPRODUCIBILITY OF RESULTS; TIME FACTORS;

EID: 82355169675     PISSN: 08936080     EISSN: 18792782     Source Type: Journal    
DOI: 10.1016/j.neunet.2011.07.006     Document Type: Article

References (41)

1. Arik S., Orman Z. Global stability analysis of Cohen-Grossberg neural networks with time varying delays. Physics Letters A 2005, 341(5-6):410-421.
2. Bai, C. (2009). Periodic oscillation for Cohen-Grossberg-type bidirectional associative memory neural networks with neutral time-varying delays. in 2009 Fifth International Conference on Natural Computation, vol. 2, (pp. 18-23).
3. Cao J., Liang J. Boundedness and stability of Cohen-Grossberg neural networks with time-varying delays. Journal of Mathematical Analysis and Applications 2004, 296(2):665-685.
4. Chen T., Rong L. Delay-independent stability analysis of Cohen-Grossberg neural networks. Physics Letters A 2003, 317(5-6):436-449.
5. Cheng C.J., Liao T.L., Yuan J.J., Hwang C.C. Globally asymptotic stability of a class of neutral type neural networks. IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics) 2006, 36(5):1191-1194.
6. Cohen M., Grossberg S. Absolute stability and global pattern formation and parallel memory storage by competitive neural networks. IEEE Transactions on Systems, Man and Cybernetics 1983, 13:815-826.
7. Cui B.T., Wu W. Global exponential stability of Cohen-Grossberg neural networks with distributed delays. Neurocomputing 2008, 72(1-3):386-391.
8. Feng J., Xu S. New criteria on global robust stability of Cohen-Grossberg neural networks with time varying delays. Neurocomputing 2008, 72(1-3):445-457.
9. Feng J., Xu S.Y., Zou Y. Delay-dependent stability of neutral-type neural networks with distributed delays. Neurocomputing 2009, 72(10-12):2576-2680.
10. Forti M., Tesi A. New conditions for global stability of neural networks with application to linear and quadratic programming problems. IEEE Transactions on Circuits and Systems I 1995, 42:345-366.
11. Jiang H.J., Cao J.D. BAM-type Cohen-Grossberg neural networks with time delays. Mathematical and Computer Modelling 2008, 47(1-2):92-103.
12. Li Y. Existence and stability of periodic solutions for Cohen-Grossberg neural networks with multiple delays. Chaos, Solitons & Fractals 2004, 20(3):459-466.
13. Liao X., Li C., Wong K. Criteria for exponential stability of Cohen-Grossberg neural networks. Neural Networks 2004, 17(10):1401-1414.
14. Liu J., Zong G.D. New delay-dependent asymptotic stability conditions concerning BAM neural networks of neutral-type. Neurocomputing 2009, 72(10-12):2549-2555.
15. Lu W.L., Chen T.P. R+n-global stability of a Cohen-Grossberg neural network system with nonnegative equilibria. Neural Networks 2007, 20(6):714-722.
16. Lu K.N., Xu D.Y., Yang Z.C. Global attraction and stability for Cohen-Grossberg neural networks with delays. Neural Networks 2006, 19(10):1538-1549.
17. Nie X.B., Cao J.D. Stability analysis for the generalized Cohen-Grossberg neural networks with inverse Lipschitz neuron activations. Computers & Mathematics with Applications 2009, 57(9):1522-1536.
18. Orman Z., Arik S. New results for global stability of Cohen-Grossberg neural networks with multiple time delays. Neurocomputing 2008, 71(16-18):3053-3063.
19. Park J.H., Kwon O.M., Lee S.M. LMI optimization approach on stability for delayed neural networks of neutral-type. Applied Mathematics and Computation 2008, 196(1):236-244.
20. Park J.H., Park C.H., Kwon O.M., Lee S.M. A new stability criterion for bidirectional associative memory neural networks of neutral-type. Applied Mathematics and Computation 2008, 199(2):716-722.
21. Qiu J., Cao J. Delay-dependent robust stability of neutral-type neural networks with time delays. Journal of Mathematical Control Science and Applications 2007, 1:179-188.
22. Rong L.B., Chen T.P. new results on the robust stability of Cohen-Grossberg neural networks with delays. Neural Process Letter 2002, 24(3):193-202.
23. Song Q.K., Cao J.D. Robust stability in Cohen-Grossberg neural networks with both time-varying and distributed delays. Neural Processing Letter 2008, 27(2):179-196.
24. Sun J., Wang L. Global exponential stability and periodic solutions of Cohen-Grossberg neural networks with continuously distributed delays. Physica D 2005, 208(1-2):1-20.
25. Wang L. Stability of Cohen-Grossberg neural networks with distributed delays. Applied Mathematics and Computation 2005, 160(1):93-110.
26. Wang Z.D., Liu Y.R., Li M. Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Transactions on Neural Networks 2006, 17(3):814-820.
27. Wang Z.D., Liu Y.R., Liu X.H. On global asymptotic stability of neural networks with discrete and distributed delays. Physics Letters A 2005, 345(4-6):299-308.
28. Wang Z.S., Zhang H.G. Global asymptotic stability of reaction-diffusion Cohen-Grossberg neural networks with continuously distributed delays. IEEE Transactions on Neural Networks 2010, 21(1):39-49.
29. Wang Z.S., Zhang H.G., Yu W. Robust stability criteria for interval Cohen-Grossberg neural networks with time varying delay. Neurocomputing 2009, 72(4-6):1105-1110.
30. Wang L., Zou X. Harmless delays in Cohen-Grossberg neural networks. Physica D 2002, 170(2):162-173.
31. Wang L., Zou X. Exponential stability of Cohen-Grossberg neural networks. Neural Networks 2002, 15(3):415-422.
32. Wu W., Cui B.T., Lou X.Y. Some criteria for asymptotic stability of Cohen-Grossberg neural networks with time varying delays. Neurocomputing 2007, 70(4-6):1085-1088.
33. Xiong W., Cao J. Global exponential stability of discrete-time Cohen-Grossberg neural networks. Neurocomputing 2005, 64:433-446.
34. Xu S., Lam J., Ho D.W.C., Zou Y. Delay-dependent exponential stability for a class of neural networks with time delays. Journal of Computational and Applied Mathematics 2005, 183(1):16-28.
35. Yu W.W., Cao J.D., Wang J. An LMI approach to global asymptotic stability of the delayed Cohen-Grossberg neural network via nonsmooth analysis. Neural Networks 2007, 20(7):810-818.
36. Zeng Z.G., Wang J. Global exponential stability of recurrent networks with time-varying delays in the presence of strong external stimuli. Neural Networks 2006, 19(10):1528-1537.
37. Zhang Y., Guo L., Feng C. Stability analysis on a neutral neural networks model. Lecture Notes in Computer Science 2005, 3644:697-706.
38. Zhang J., Suda Y., Komine H. Global exponential stability of Cohen-Grossberg neural networks with variable delays. Physics Letters A 2005, 338(1):44-50.
39. Zhang H.G., Wang Z.S., Liu D.R. Global asymptotic stability and robust stability of a class of Cohen-Grossberg neural networks with mixed delays. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 2009, 56(3):616-629.
40. Zhang Z.Q., Zhou D.M. Global robust exponential stability for second-order Cohen-Grossberg neural networks with multiple delays. Neurocomputing 2009, 73(1-3):213-218.
41. Zhao H.Y., Wang L. Hopf bifurcation in Cohen-Grossberg neural network with distributed delays. Nonlinear Analysis. Real World Applications 2007, 8(1):73-89.