Boundedness and global convergence of non-autonomous neural networks with variable delays

Nonlinear Analysis: Real World Applications

Volumn 10, Issue 4, 2009, Pages 2195-2206

  Yuan, Zhaohui ^a   Yuan, Lifen ^b   Huang, Lihong ^a   Hu, Dewen ^c  

^a HUNAN UNIVERSITY   (China)

^b HUNAN NORMAL UNIVERSITY   (China)

^c NATIONAL UNIVERSITY OF DEFENSE TECHNOLOGY   (China)

Author keywords

Asymptotic system; Boundedness; Convergence; Delay; Neural networks

Indexed keywords

ASYMPTOTIC ANALYSIS; ELECTRIC NETWORK ANALYSIS; HOPFIELD NEURAL NETWORKS; TIME VARYING NETWORKS;

ANALYSIS METHODS; ASYMPTOTIC SYSTEM; BOUNDEDNESS; CONVERGENCE; DELAY; DELAYED HOPFIELD NEURAL NETWORKS; GLOBAL CONVERGENCES; INEQUALITY TECHNIQUES; M MATRIXES; NON-AUTONOMOUS NEURAL NETWORKS; NON-AUTONOMOUS SYSTEMS; NUMERICAL SIMULATIONS; SUFFICIENT CONDITIONS; TIME-VARYING; VARIABLE DELAYS;

NEURAL NETWORKS;

EID: 61749089753     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2008.04.004     Document Type: Article

References (29)

1. Bouzerdoum A., and Pattison T.R. Neural network for quadratic optimization with bound constraints. IEEE Trans. Neural Netw. 4 (1993) 293-303
2. Haykin S. Neural Networks: A Comprehensive Foundation (1994), Macmillan, New York
3. Hertz J.A., Krogh A., and Palmer R.G. Introduction to Theory of Neural Computation (1994), Addison-Wesley, Reading, MA
4. Hopfield J.J. Neural networks and physical systems with emergent collective computational abilities. Proc. Nat. Acad. Sci. 79 (1982) 2554-2558
5. Hopfield J.J., and Tank D.W. Computing with neural circuits: A model. Science 233 (1986) 625-633
6. Kosko B. Bidirectional associative memories. IEEE Trans. Syst., Man Cybern. 18 (1998) 49-60
7. Xu Z.B., and Kwong C.P. Associative memories. In: Leondes C.T. (Ed). Neural Networks Systems: Techniques and Applications vol. 3 (1998), Academic Press, New York 183-258
8. Marcus C.M., and Westervelt R.M. Stability of analog neural networks with delay. Phys. Rev. A 39 (1989) 347-359
9. Cao J., and Liang J. Boundedness and stability for Cohen-Grossberg neural networks with time-varying delays. J. Math. Anal. Appl. 296 (2004) 665-685
10. Yuan Z., Hu D., Huang L., and Dong G. On the global asymptotic stability analysis of delayed neural networks. Int. J. Bifurcation Chaos 15 (2005) 4019-4025
11. Yuan Z., Hu D., Huang L., and Dong G. Existence and global exponential stability of periodic solution for CohenCGrossberg neural networks with delays. Nonlinear Anal.: Real World Appl. 7 (2006) 572-590
12. Huang C., Huang L., and Yuan Z. Global stability analysis of a class of delayed cellular neural networks. Math. Comput. Simul. 70 (2005) 133-148
13. Chen T. Global exponential stability of delayed Hopfield neural networks. Neural Netw. 14 (2001) 977-980
14. Forti M. On global asymptotic stability of a class of nonlinear systems arising in neural network theory. J. Differential Equations 113 (1994) 246-264
15. Arik S. Stability analysis of delayed neural networks. IEEE Trans. Circuits Syst. 47 (2000) 1089-1092
16. van den Driessche P., and Zou X. Global attractivity in delayed Hopfield neural network models. SIAM J. Appl. Math. 58 (1998) 1878-1890
17. Wang L. Stabilizing Hopfield neural networks via inhibitory self-connections. J. Math. Anal. Appl. 292 (2004) 135-147
18. Liu B., and Huang L. Existence and exponential stability of almost periodic solutions for cellular neural networks with time-varying delays. Phys. Lett. A 341 (2005) 135-144
19. Zhou J., Liu Z., and Chen G. Dynamics of periodic delayed neural networks. Neural Netw. 17 (2004) 87-101
20. Chen T., Lu W., and Chen G. Dynamical behavior of a large class of general delayed neural networks. Neural Comput. 17 (2005) 949-974
21. Zheng W., and Zhang J. Global exponential stability of a class of neural networks with variable delays. Comput. Math. Appl. 49 (2005) 895-902
22. Zheng Y., and Chen T. Global exponential stability of delayed periodic dynamical systems. Phys. Lett. A 322 (2004) 344-355
23. Chu T. An exponential convergence estimate for analog neural networks with delay. Phys. Lett. A 283 (2001) 113-118
24. Cao J. An estimation of the domain of attraction and convergence rate for Hopfield continuous feedback neural networks. Phys. Lett. A 325 (2004) 370-374
25. Zhao H., and Wang G. Delay-independent exponential stability of recurrent neural networks. Phys. Lett. A 333 (2004) 399-407
26. Liu B., and Huang L. Existence and exponential stability of periodic solutions for cellular neural networks with time-varying delays. Phys. Lett. A 349 (2006) 474-483
27. So J.W.-H., Tang X., and Zou X. Stability in linear delay system without instantaneous negative feedback. SIAM J. Math. Anal. 33 (2002) 1297-1304
28. Chen Y. Global stability of neural networks with distributed delays. Neural Netw. 15 (2002) 867-871
29. Shampine L.F., and Thompson S. Solving DDEs in Matlab. Appl. Numer. Math. 37 (2001) 441-458