Global exponential stability and existence of periodic oscillatory solutions for reaction-diffusion generalized neural networks with time-varying delays

Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms

Volumn 14, Issue 3, 2007, Pages 371-384

  Zhao, Zhenjiang ^a   Song, Qiankun ^a,b   Li, Yongmin ^a  

^a HUZHOU UNIVERSITY   (China)

^b CHONGQING JIAOTONG UNIVERSITY   (China)

Author keywords

Generalized neural networks; Global exponential stability; Nonsingular M matrix; Periodic oscillatory solution; Reaction diffusion; Time varying delays

Indexed keywords

EID: 34248597370     PISSN: 14928760     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (29)

1. S. Arik and V. Tavsanoglu, Equilibrium analysis of delayed CNNS, IEEE Trans. Circuits Syst. I, 45, (1998) 168-171.
2. J. D. Cao, Global Stability analysis in delayed cellular neural networks, Phys. Rev. E, 59, (1999) 5940-5944.
3. J. D. Cao, Exponential stability and periodic solution of delayed cellular neural networks, Science in China(in Chinese, Series E), 43, (2000) 328-336.
4. J. D. Cao, New results Concerning Exponential Stability and Periodic solutions of delayed cellular neural networks, Phys. Lett. A, 307, (2003) 136-147.
5. J. D. Cao, Global exponential stability of Hopfield neural networks, Int. J. Systems Sci., 32, (2001) 233-236.
6. J. D. Cao, Exponential stability and periodic oscillatory solution in BAM networks with delays. IEEE Trans. Neural Networks, 13, (2002) 457-463.
7. J. D. Cao and J. Wang, Global Asymptotic Stability of a General Class of recurrent neural networks with time-varying delays, IEEE Trans. Circuits Syst. I, 50, (2003) 34-44.
8. J. D. Cao and L. Wang, Periodic oscillatory solution of bidirectional associative memory networks with delays, Phys. Rev. E. 61, (2000) 1825-1828.
9. J. D. Cao and D. Zhou, Stability analysis of delayed cellular neural networks. Neural Networks, 11, (1998) 1601-1605.
10. G. A. Carpenter, A geometric approach to singular perturbation problems with application to nerve impulse equations, J. Differential Equations, 23, (1977) 355-367.
11. A. P. Chen, L. H. Huang, J. D. Cao, Existence and stability of almost periodic solution for BAM neural networks with delays, Appl. Math. Comput., 137, (2003) 177-193.
12. L. O. Chua and L. Yang, Cellular neural networks: Theory, IEEE Trans. Circuits Syst., 35, (1988) 1257-1272.
13. J. W. Evans, Nerve axon equations II: Stability at rest, Indiana Univ. Math. J., 22, (1972) 75-90.
14. M. Forti and A. Tesi, New conditions for global stability of neural networks with application to linear and quadratic programming problems, IEEE Trans. Circuits Syst. I, 42, (1995) 354-366.
15. M. Gilli, Stability of cellular neural networks and delayed cellular neural networks with Non-positive templates and Non-monotonic output functions, IEEE Trans. Circuits Syst. I, 41, (1994) 518-528.
16. Q. M. He and L. S. Kang, Existence and Stability of global solution for generalized Hopfield neural networks system, Neural Parallel Sci. Comput., 2, (1994) 165-176.
17. H. Huang and J. D. Cao, On global asymptotic stability of recurrent neural networks with time-varying delays. Appl. Math. Comput., 142, (2003) 143-154.
18. H. Huang, J. D. Cao, J. Wang, Global exponential stability and periodic solutions of recurrent neural networks with delays, Phys. Lett. A, 298, (2002) 393-404.
19. J. L. Liang and J. D. Cao, Global exponential stability of reaction-diffusion recurrent neural networks with time-varying delays, Phys. Lett. A, 314, (2003) 434-442.
20. X. X. Liao, Mathematical theory of CNNs (II), Science in China(in Chinese, Series A), 24, (1994) 1037-1046.
21. X. X. Liao, Y. L. Fu, J. Gao, Z. Q. Zhao, Stability of Hopfield neural networks with reaction-diffusion terms, Acta Electron. Sinica, 28, (2000)78-80.
22. X. X. Liao, S. Z. Yang, S. J. Cheng, Y. Shen, Stability of Generalized networks with reaction-diffusion terms, Science in China(in Chinese, Series E), 32, (2002)87-94.
23. T. Roska and L. O. Chua, Cellular neural networks with nonlinear and delay-type template, Int. J. Circuit Theory Appl., 20. (1992) 469-481.
24. T. Roska, C. W. Wu, M. Balsi, L. O. Chua, Stability and Dynamics of delay-type general and Cellular Neural Networks, IEEE Trans. Circuits Syst. I, 39, (1992) 487-490.
25. T. Roska, C. W. Wu, L. O. Chua, Stability of Cellular Neural Networks with dominant nonlinear and delay-type template, IEEE Trans. Circuits Syst. I, 40, (1993) 270-272.
26. Q. K. Song and J. D. Cao, Global exponential stability and existence of periodic solutions in BAM networks with delays and reactionCdiffusion terms, Chaos, Solitons and Fractals, 23, (2005) 421-430.
27. C. Y. Sun, K. Zhang, S. Fei, C. B. Feng, On exponential stability of delayed neural networks with a general class of activation functions, Phys. Lett. A, 298, (2002) 122-132.
28. L. S. Wang and D. Y. Xu, Global exponential stability of Hopfield reaction-diffusion neural networks with time-varying delays, Science in China(Series F), 46, (2003) 466-474.
29. J. Zhang and X. S. Jin, Global stability analysis in delayed Hopfield Neural Network models, Neural Networks, 13, (2000) 745-753.