Periodic solution for nonautonomous bidirectional associative memory neural networks with impulses

Neurocomputing

Volumn 70, Issue 13-15, 2007, Pages 2517-2527

  Gui, Zhanji ^a,b   Yang, Xiao Song ^a   Ge, Weigao ^c  

^a HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b HAINAN NORMAL UNIVERSITY   (China)

^c BEIJING INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Global exponential stability; Impulsive effect; Neural networks; Periodic solution; Quasi periodic solution; Simulation method

Indexed keywords

ASSOCIATIVE STORAGE; ASYMPTOTIC STABILITY; COMPUTER SIMULATION; GLOBAL OPTIMIZATION;

BIDIRECTIONAL ASSOCIATIVE MEMORY; GLOBAL EXPONENTIAL STABILITY; IMPULSIVE EFFECT; PERIODIC SOLUTION;

NEURAL NETWORKS;

ARTICLE; ASSOCIATIVE MEMORY; MATHEMATICAL MODEL; NERVE CELL NETWORK; NERVE CONDUCTION; OSCILLATION; PRIORITY JOURNAL; PROBLEM SOLVING; SIMULATION; THEORY;

EID: 34249704035     PISSN: 09252312     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neucom.2006.08.004     Document Type: Article

References (37)

1. Akca̧ H., Alassar R., Covachev V., Covacheva Z., and Al-Zahrani E. Continuous-time additive Hopfield-type neural networks with impulses. J. Math. Anal. Appl. 290 (2004) 436-451
2. Arika S., and Tavsanoglu V. Global asymptotic stability analysis of bidirectional associative memory neural networks with constant time delays. Neurocomputing 68 (2005) 161-176
3. Bainov D.D., and Simeonov P.S. Stability Theory of Differential Equations with Impulse Effects: Theory and Applications (1989), Ellis Horwood, Chichester
4. Bouzerdoum A., Y Zhang T.R.J., and Yang YR. Global stability analysis of bi-directional associative memory neural networks with time delay. Int. J. Circuit Theory Appl. 29 2 (2001) 185-196
5. Cao J., and Jiang Q. An analysis of periodic solutions of bi-directional associative memory networks with time-varying delays. Phys. Lett. A 330 (2004) 203-213
6. Cao J., and Liang J. Boundedness and stability for Cohen-Grossberg neural networks with time-varying delays. J. Math. Anal. Appl. 296 2 (2004) 665-685
7. Cao J., Liang J., and Lam J. Exponential stability of high-order bidirectional associative memory neural networks with time delays. Physica D 199 (2004) 425-436
8. Cao J., and Song Q. Stability in Cohen-Grossberg type BAM neural networks with time-varying delays. Nonlinearity 19 7 (2006) 1601-1617
9. Cao J., and Wang L. Exponential stability and periodic oscillatory solution in BAM networks with delays. IEEE Trans. Neural Networks 13 (2002) 456-463
10. Chen A.P., Cao J.D., and Huang L.H. Exponential stability of BAM neural networks with transmission delays. Neurocomputing 57 (2004) 435-454
11. Chen A., Huang L., and Cao J. Existence and stability of almost periodic solution for BAM neural networks with delays. Appl. Math. Comput. 137 (2003) 177-193
12. Dong Y., and Zhou E. An application of coincidence degree continuation theorem in existence of solutions of impulsive differential equations. J. Math. Anal. Appl. 197 (1996) 875-889
13. Gaines R.E., and Mawhin J.L. Coincidence Degree and Nonlinear Differential equations (1977), Springer, Berlin
14. Gopalsamy K. Stability of artificial neural networks with impulses. Appl. Math. Comput. 154 (2004) 783-813
15. Guan Z., Chen G., and Qin Y. On equilibria, stability and instability of Hopfield neural networks. IEEE Trans. Neural Networks 2 (2000) 534-540
16. Guan Z., James L., and Chen G. On impulsive auto-associative neural networks. Neural Networks 13 (2000) 63-69
17. Guan Z., Liu Y., and Wen X. Decentralized stabilization of singular and time-delay large-scale control systems with impulsive solutions. IEEE Trans. Automat. Control 40 (1995) 1437-1441
18. Gui Z. Biological Dynamic Models and Computer Simulation (2005), Science Press, Beijing
19. Huang X., Cao J., and Huang D. LMI-based approach for delay-dependent exponential stability analysis of BAM neural networks. Chaos, Solitons & Fractals 24 (2005) 885-898
20. Jiang H., Li Z., and Teng Z. Boundedness and stability for nonautonomous cellular neural networks with delay. Phys. Lett. A 306 (2003) 313-325
21. Kosko B. Adaptive bidirectional associative memories. Appl. Opt. 26 (1987) 4947-4960
22. Kosko B. Bidirectional associative memories. IEEE. Trans. Syst. Man Cybern. SMC 18 (1988) 49-60
23. Kosko B. Unsupervised learning in noise. IEEE Trans. Neural Networks 1 (1990) 44-57
24. Lakshmikantham V., Bainov D.D., and Simeonov P.S. Theory of Impulse Differential Equations (1989), World Scientific, Singapore
25. Li Y. Global exponential stability of BAM neural networks with delays and impulses. Chaos, Solitons and Fractals 24 (2005) 279-285
26. Li Y., and Lu L. Global exponential stability and existence of periodic solution of Hopfield-type neural networks with impulses. Phys. Lett. A 333 (2004) 62-71
27. Li Y., Xing W., and Lu L. Existence and global exponential stability of periodic solution of a class of neural networks with impulses. Chaos, Solitons and Fractals 27 (2006) 437-445
28. Liao X., and Li C. An LMI approach to asymptotical stability of multi-delayed neural networks. Physica D 200 (2005) 139-155
29. Liu Z., Chen A., and Huang L. Existence and global exponential stability of periodic solution to self-connection BAM neural networks with delays. Phys. Lett. A 328 (2004) 127-143
30. Liu Z., and Liao L. Existence and global exponential stability of periodic solution of cellular neural networks with time-varying delays. J. Math. Anal. Appl. 290 (2004) 247-262
31. Mohamad S. Global exponential stability in continuous-time and discrete-time delayed bidirectional neural networks. Physica D 159 (2001) 233-251
32. Pandit S.G., and Deo S.G. Differential Systems Involving Impulses (1982), Springer, New York
33. Rehim M., Jiang H., and Teng Z. Global exponential stability of cellular neural networks with varying-time coefficients and delays. Neural Networks 17 (2004) 1017-1025
34. Sun J.T., Zhang Y.P., and Wu Q.D. Less conservative conditions for asymptotic stability of impulsive control systems. IEEE Trans. Automat. Control 48 (2003) 829-831
35. Zhang Y., and Sun J.T. Stability of impulsive neural networks with delays. Phys. Lett. A 348 (2005) 44-50
36. Zhao H. Exponential stability and periodic oscillatory of bi-directional associative memory neural network involving delays. Neurocomputing 69 (2006) 424-448
37. Zhou J., Liu Z., and Chen G. Dynamics of periodic delayed neural networks. Neural Networks 17 (2004) 87-101