Periodic solutions and its exponential stability of reaction-diffusion recurrent neural networks with continuously distributed delays

Nonlinear Analysis: Real World Applications

Volumn 7, Issue 1, 2006, Pages 65-80

  Song, Qiankun ^a   Cao, Jinde ^b   Zhao, Zhenjiang ^a  

^a HUZHOU UNIVERSITY   (China)

^b SOUTHEAST UNIVERSITY   (China)

Author keywords

Distributed delays; Global exponential stability; Lyapunov functional; Periodic oscillatory solutions; Reaction diffusion; Recurrent neural networks

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DIFFUSION; LYAPUNOV METHODS;

DISTRIBUTED DELAYS; GLOBAL EXPONENTIAL STABILITY; LYAPUNOV FUNCTIONAL; PERIODIC OSCILLATORY SOLUTIONS; REACTION DIFFUSION;

RECURRENT NEURAL NETWORKS;

EID: 24944581606     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2005.01.004     Document Type: Article

References (37)

1. S. Arik V. Tavsanoglu Equilibrium analysis of delayed CNNS IEEE Trans. Circuits and Systems I 45 1998 168-171
2. P. Baldi A.F. Atiya How delays affect neural dynamics and learning IEEE Trans. Neural Networks 5 1994 312-621
3. J.D. Cao Global Stability analysis in delayed cellular neural networks Phys. Rev. E 59 1999 5940-5944
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 J. Wang Global asymptotic stability of a general class of recurrent neural networks with time-varying delays IEEE Tran. Cricuit and Systems I 50 2003 34-44
6. J.D. Cao J. Wang Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays Neural Netwoks 17 2004 379-390
7. J.D. Cao D.M. Zhou Stability analysis of delayed cellular neural networks Neural Networks 11 1998 1601-1605
8. G. Carpenter A geometric approach to singular perturbation problems with application to nerve implus equations J. Differential Equations 23 1977 355-367
9. L.O. Chua L. Yang Cellular neural networks: Theory IEEE Trans. Circuits and Systems 35 1988 1257-1272
10. M.A. Cohen S. Grossberg Absolute stability of global pattern formation and parallel memory storage by competitive neural networks IEEE Trans. Systems Man. Cybernet 35 1983 815-826
11. J.W. Evans Nerve axon equs II: Stability at Rest Indiana Univ. Math. J. 22 1973 75-90
12. K. Gopalsamy X.Z. He Stability in asymmetric Hopfield nets with transmission delays Physica D 76 1994 344-358
13. A. Hastings Global Stability in Lotka-Volterra systems with diffusion J. Math. Biol. 6 1978 163-168
14. Q.M. He L.S. Kang Existence and Stability of global solution for generalized Hopfield neural networks system Neural Parallel Sci. Comput. 2 1994 165-176
15. J.J. Hopfield Neurons with graded response have collective computational properties like those of two-state neurons Proc. Nat. Acad. Sci. USA 81 1984 3088-3092
16. J.J. Hopfield D.W. Tank Computing with neural circuits: A model Science 233 1986 625-633
17. J.L. Liang J.D. Cao Global exponential stability of reaction-diffusion recurrent neural networks with time-varying delays Phys. Lett. A 314 2003 434-442
18. C.M. Marcuss R.M. Westervelt Stability of analog neural networks with delay Phys. Rev. A 39 1989 347-359
19. S. Mohamad K. Gopalsamy Dynamics of a class of discrete-time neurals networks and their continuous-time counterparts Math. Comput. Simulat. 53 2000 1-39
20. V.S.H. Rao Bh.R.M. Phaneendra Global dynamics of bidirectional associative memory neural networks involving transmission delays and dead Zones Neural Networks 12 1999 455-465
21. T. Roska C.W. Wu M. Balsi L.O. Chua Stability and dynamics of delay-type general and cellular neural networks IEEE Trans. Circuits and Systems I 39 1992 487-490
22. T. Roska C.W. Wu L.O. Chua Stability of cellular neural networks with dominant nonlinear and delay-type templates IEEE Trans. Circuits and Systems I 40 1993 270-272
23. F. Rothe Convergence to the equilibrium state in the Volterra-Lotka diffusion equations J. Math. Biol. 3 1976 319-324
24. L.S. Wang D.Y. Xu Global exponential stability of Hopfield reaction-diffusion neural networks with variable delays Sci. China Ser. F 46 2003 466-474
25. J.Y. Zhang Global exponential stability of neural networks with variable delays IEEE Trans. Circuits and Systems I 50 2003 288-290
26. J.Y. Zhang X.S. Jin Global stability analysis in delayed Hopfield Neural Network models Neural Networks 13 2000 745-753
27. Q. Zhang X.P. Wei J. Xu Global exponential stability of Hopfield neural networks with continuously distributed delays Phys. Lett. A 315 2003 431-436
28. H.Y. Zhao Global stability of bidirectional associative memory neural networks with distributed delays Phys. Lett. A 297 2002 182-190
29. J.D. Cao J.L. Liang Boundedness and stability for Cohen-Grossberg neural networks with time-varying delays J. Math. Anal. Appl. 296 2004 665-685
30. J.D. Cao D.W.C. Ho A general framework for global asympotic stability analysis of delayed neural networks based on LMI approach Chaos, Solitons and Fractals 24 2005 1317-1329
31. J.D. Cao D.-S. Huang Y.Z. Qu Global robust stability of delayed recurrent neural networks Chaos, Solitons and Fractals 23 2005 221-229
32. J.D. Cao J.L. Liang J. Lam Exponential stability of high-order bidirectional associative memory neural networks with time delays Physica D 199 2004 425-436
33. J.D. Cao Periodic solutions and exponential stability in delayed cellular neural networks Physical Review E 60 1999 3244-3248
34. J.D. Cao Global stability conditions for delayed CNNs IEEE Trans. Circuits and Systems I 48 2001 1330-1333
35. J.D. Cao A set of stability criteria for delayed cellular neural networks IEEE Trans. Circuits and Systems I 48 2001 494-498
36. J.D. Cao Exponential stability and periodic solution of delayed cellular neural networks, Sci. China Ser. E 43 2000 328-336
37. J.D. Cao J. Wang X.F. Liao Novel stability criteria of delayed cellular neural networks, Int. J. Neural Systems 13 2003 367-375