Existence and globally exponential stability of periodic solution of BAM neural networks with impulses and recent-history distributed delays

Neurocomputing

Volumn 71, Issue 4-6, 2008, Pages 813-822

  Gu, Haibo ^a   Jiang, Haijun ^a   Teng, Zhidong ^a  

^a XINJIANG UNIVERSITY   (China)

Author keywords

Globally exponential stability; Impulses; Neural networks; Periodic solution

Indexed keywords

ASYMPTOTIC STABILITY; LYAPUNOV FUNCTIONS;

BI-DIRECTIONAL ASSOCIATIVE MEMORY; FIXED POINT THEOREM; GLOBALLY EXPONENTIAL STABILITY; PERIODIC SOLUTION;

NEURAL NETWORKS;

ARTICLE; ARTIFICIAL NEURAL NETWORK; ASSOCIATIVE MEMORY; BIDIRECTIONAL ASSOCIATIVE MEMORY; COMPUTER ANALYSIS; COMPUTER NETWORK; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MATHEMATICAL VARIABLE; METHODOLOGY; NERVE CONDUCTION; PRIORITY JOURNAL;

EID: 38649094006     PISSN: 09252312     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neucom.2007.03.007     Document Type: Article

References (25)

1. Akca H., Alassar R., Covachev V., Covacheva Z., and Al-Zahrani E. Continuous-time Hopfield-type neural networks with impulses. J. Math. Anal. Appl. 290 (2004) 436-451
2. Arik S., and Tavsanoglu V. Global asymptotic stability analysis of bidirectional associative memory neural networks with constant time delays. Neurocomputing 68 (2005) 161-171
3. Cao J. Global asymptotic stability of delayed bi-directional associative memory neural networks. Appl. Math. Comput. 142 (2003) 333-339
4. Cao J., and Dong M.F. Exponential stability of delayed bi-directional associative memory networks. Appl. Math. Comput. 135 (2003) 105-112
5. Cao J., Ho D., and Huang X. LMI-based criteria for global robust stability of bidirectional associative memory networks with time delay. Nonlinear Anal. 66 (2007) 1558-1572
6. Cao J., and Jiang Q.H. An analysis of periodic solutions of bi-directional associative memory networks with time-varying delays. Phys. Lett. A 330 (2004) 203-213
7. Cao J., Liang J.L., and Lam J. Exponential stability of high-order bidirectional associative memory neural networks with time delays. Physica D 199 (2004) 425-436
8. Gopalsamy K. Stability of artificial neural networks with impulses. Appl. Math. Comput. 154 (2004) 783-813
9. Guan Z., and Chen G. On delayed impulsive Hopfield neural networks. Neural Networks 12 (1999) 273-280
10. Guan Z., Chen G., and Qin Y. On equilibria, stability and instability of Hopfield neural networks. Neural Networks 2 (2000) 534-540
11. Guan Z., Lam J., and Chen G. On impulsive autoassociative neural networks. Neural Networks 13 (2000) 63-69
12. Gui Z.J., and Ge W.G. Existence and uniqueness and periodic solutions of nonautonomous cellular neural networks with impulses. Phys. Lett. A 354 (2006) 84-94
13. Gui Z.J., and Ge W.G. Periodic solutions of nonautonomous cellular neural networks with impulses. Chaos, Solitons Fractals 32 5 (2007) 1760-1771
14. Hopfield J. Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. USA 79 (1982) 2554-2558
15. Kosko B. Adaptive bi-directional associative memories. Appl. Optim. 26 (1987) 4947-4960
16. Lakshimikanthan V., Bainov D.D., and Simeonov P.S. Theory of Impulsive Differential Equations (1989), World Scientific, Singapore
17. Lasalle J.P. The Stability of Dynamical System (1976), SIAM, Philadelphia
18. Li Y. Global exponential stability of BAM neural networks with delays and impulses. Chaos Solitons Fractal 24 (2005) 279-285
19. 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
20. Li Y.T., and Yang C.B. Global exponential stability analysis on impulsive BAM neural networks with distributed delays. J. Math. Anal. Appl. 324 (2006) 1125-1139
21. Liu B.W., and Huang L. Global exponential stability of BAM neural networks with recent-history distributed delays and impulses. Neurocomputing 69 (2006) 2090-2096
22. Lou X.Y., and Cui B.T. Global asymptotic stability of delay BAM neural networks with impulses. Chaos Solitons Fractal 29 (2006) 1023-1031
23. Wang H., Liao X.F., and Li C. Existence and exponential stability of periodic solution of BAM neural networks with impulse and time-varying delay. Chaos, Solitons Fractals 33 3 (2007) 1028-1039
24. Xu D.Y., and Yang Z. Impulsive differential inequality and stability of neural networks, bidirectional associative memories. J. Math. Anal. Appl. 305 (2005) 107-120
25. Yang X.F., Liao X.F., Evans D., and Tang Y. Existence and stability of periodic solution in impulsive Hopfield neural networks with finite distributed delays. Phys. Lett. A 343 (2005) 108-116