Existence and globally exponential stability of equilibrium for fuzzy BAM neural networks with distributed delays and impulse

Advances in Difference Equations

Volumn 2011, Issue , 2011, Pages

  Zhang, Qianhong ^a   Yang, Lihui ^b   Liao, Daixi ^c  

^a GUIZHOU UNIVERSITY OF FINANCE AND ECONOMICS   (China)

^b HUNAN CITY UNIVERSITY   (China)

^c HUNAN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Distributed delays; Equilibrium point; Fuzzy BAM neural networks; Globally exponential stability; Impulse

Indexed keywords

EID: 84868089995     PISSN: 16871839     EISSN: 16871847     Source Type: Journal    
DOI: 10.1186/1687-1847-2011-8     Document Type: Article

References (35)

1. Kosto, B: Adaptive bi-directional associative memories. Appl Opt. 26, 4947-4960 (1987). doi:10.1364/AO.26.004947
2. Kosto, B: Bi-directional associative memories. IEEE Trans Syst Man Cyber. 18, 49-60 (1988). doi:10.1109/21.87054
3. Gopalsmy, K, He, XZ: Delay-independent stability in bi-directional associative memory networks. IEEE Trans Neural Netw. 5, 998-1002 (1994). doi:10.1109/72.329700
4. Liu, B, Huang, L: Global exponential stability of BAM neural networks with recent-history distributed delays and impulse. Neurocomputing. 69, 2090-2096 (2006). doi:10.1016/j.neucom.2005.09.014
5. Cao, J, Wang, L: Exponential stability and periodic oscilatory solution in BAM networks with delays. IEEE Trans Neural Netw. 13, 457-463 (2002). doi:10.1109/72.991431
6. Zhao, H: Global exponential stability of bidirectional associative memory neural networks with distributed delays. Phys Lett A. 297, 182-190 (2002). doi:10.1016/S0375-9601(02)00434-6
7. Zhang, J, Yang, Y: Global stability analysis of bidirectional associative memory neural networks with time delay. Int J Ciruit Theor Appl. 29, 185-196 (2001). doi:10.1002/cta.144
8. Liao, XF, Wong, KW, Yang, SZ: Convergence dynamics of hybrid bidirectional associative memory neural networks with distributed delays. Phys Lett A. 316, 55-64 (2003). doi:10.1016/S0375-9601(03)01113-7
9. Liao, XF, Yu, JB: Qualitative analysis of bi-directional associative memory with time delay. Int J Circ Theory Appl. 26, 219-229 (1988)
10. Cao, J, Jiang, Q: An analysis of periodic solutions of bi-directional associative memory networks with time-varying delays. Phys Lett A. 330, 203-213 (2004). doi:10.1016/j.physleta.2004.07.064
11. Chen, A, Cao, J, Huang, L: Exponential stability of BAM neural networks with transmission delays. Neurocomputing. 57, 435-454 (2004)
12. Chen, A, Huang, L, Cao, J: Existence and stability of almost periodic solution for BAM neural networks with delays. Appl Math Comput. 137, 177-193 (2003). doi:10.1016/S0096-3003(02)00095-4
13. Chen, A, Huang, L, Liu, Z, Cao, J: Periodic bidirectional associative memory neural networks with distributed delays. J Math Anal Appl. 317, 80-102 (2006). doi:10.1016/j.jmaa.2005.09.092
14. Liu, Z, Chen, A, Cao, J, Huang, L: Existence and global exponential stability of almost periodic solutions of BAM neural networks with continuously distributed delays. Phys Lett A. 319, 305-316 (2003). doi:10.1016/j.physleta. 2003.10.020
15. Guo, SJ, Huang, L, Dai, B, Zhang, Z: Global existence of periodic solutions of BAM neural networks with variable coefficients. Phys Lett A. 317, 97-106 (2003). doi:10.1016/j.physleta.2003.08.019
16. Cao, J: A set of stability criteria for delayed cellular neural networks. IEEE Trans Circuits Syst I. 48, 494-498 (2001). doi:10.1109/81.917987
17. Cao, J: Global stability conditions for delayed CNNs. IEEE Trans Circuits Syst I. 48, 1330-1333 (2001). doi:10.1109/81.964422
18. Cao, J, Wang, J: Global asymptotic stability of general class of recurrent neural networks with time-varying delays. IEEE Trans Circuits Syst I. 50, 34-44 (2003). doi:10.1109/TCSI.2002.807494
19. Cao, J: New results concerning exponential stability and periodic solutions of delayed cellular neural networks. Phys Lett A. 307, 136-147 (2003). doi:10.1016/S0375-9601(02)01720-6
20. Cao, J, Wang, J: Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays. Neural Netw. 17, 379-390 (2004). doi:10.1016/j.neunet.2003.08.007
21. Cao, J, Wang, J: Global exponential stability and periodicity of recurrent neural networks with time delays. IEEE Trans Circuits Syst I. 52, 920-931 (2005)
22. Cao, J, Ho, DWC: A general framework for global asymptotic stability analysis of delayed neural networks based on LMI approach. Chaos Solitons Fract. 24, 1317-1329 (2005). doi:10.1016/j.chaos.2004.09.063
23. Cao, J, Huang, D, Qu, Y: Global robust stability of delayed recurrent neural networks. Chaos Solitons Fract. 23, 221-229 (2005). doi:10.1016/j.chaos. 2004.04.002
24. Yang, T, Yang, L: The global stability of fuzzy cellular neural networks. IEEE Trans Circuit Syst I. 43, 880-883 (1996). doi:10.1109/81.538999
25. Yang, T, Yang, L, Wu, C, Chua, L: Fuzzy cellular neural networks: theory. Proceedings of the IEEE International Workshop on Cellular Neural Networks Application. 181-186 (1996)
26. Yang, T, Yang, L, Wu, C, Chua, L: Fuzzy cellular neural networks: applications. Proceedings of IEEE International Workshop on Cellular Neural Neworks Application. 225-230 (1996)
27. Huang, T: Exponential stability of fuzzy cellular neural networks with distributed delay. Phys Lett A. 351, 48-52 (2006). doi:10.1016/j.physleta.2005. 10.060
28. Huang, T: Exponential stability of delayed fuzzy cellular neural networks with diffusion. Chaos Solitons Fract. 31, 658-664 (2007). doi:10.1016/j.chaos. 2005.10.015
29. Yuan, K, Cao, J, Deng, J: Exponential stability and periodic solutions of fuzzy cellular neural networks with time-varying delays. Neurocomputing. 69, 1619-1627 (2006). doi:10.1016/j.neucom.2005.05.011
30. Zhang, Q, Xiang, R: Global asymptotic stability of fuzzy cellular neural networks with time-varying delays. Phys Lett A. 372, 3971-3977 (2008). doi:10.1016/j.physleta.2008.01.063
31. Lakshmikantham, V, Bainov, DD, Simeonov, P: Theory of impulsive differential equations. World Sceintific, Singaore (1989)
32. Liu, X, Ballinger, G: Existence and continuability of solutions for differential equations with delays and state-dependent mpulses. Nonlinear Anal. 51, 633-647 (2002). doi:10.1016/S0362-546X(01)00847-1
33. Yan, JR, Zhao, A, Yan, W: Existence and global attractivity of periodic solution for an impulsive delay differentia equation with Allee effect. J Math Anal Appl. 309, 489-504 (2005). doi:10.1016/j.jmaa.2004.09.038
34. Li, YK: Global exponential stability of BAM neural networks with delays and impulses. Chaos, Solitons Fract. 24, 279-285 (2005)
35. Li, YK, Gao, S: Global exponential stability for impulsive BAM neural networks with distributed delays on time scales. Neural Process Lett. 31, 65-91 (2010). doi:10.1007/s11063-009-9127-z