Global exponential stability for a class of generalized neural networks with distributed delays

Nonlinear Analysis: Real World Applications

Volumn 5, Issue 3, 2004, Pages 527-547

  Liao, Xiaofeng ^a,b   Wong, Kwok wo ^c   Li, Chunguang ^b  

^a CHONGQING UNIVERSITY   (China)

^b UNIVERSITY OF ELECTRONIC SCIENCE AND TECHNOLOGY OF CHINA   (China)

^c CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Distributed delays; Generalized neural networks; Global asymptotic stability; Global exponential stability; Lyapunov functionals

Indexed keywords

EID: 1542507110     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2003.12.002     Document Type: Article

References (30)

1. Baldi P. Atiya A.F. How delays affect neural dynamics and learning IEEE Trans. Neural Networks 5 1994 612-621
2. Y.M. Chen, Global stability of neural networks with distributed delays, Neural Networks (2002).
3. De Vries B. Principle J.C. The gamma model - A new neural model for temporal processing Neural Networks 5 1992 565-576
4. Feng C.H. Plamondon R. On the stability analysis of delayed neural networks systems Neural Networks 14 2001 1181-1188
5. Forti M. On global asymptotic stability of a class of nonlinear systems arising in neural network theory J. Differential Equations 113 1994 246-264
6. Gopalsamy K. He X.Z. Stability in asymmetric Hopfield networks with transmission delays Physica D 76 1994 344-358
7. Gopalsamy K. He X.Z. Delay-independent stability in bidirectional associative memory networks IEEE Trans. Neural Networks 5 1994 998-1002
8. J.K. Hale, S.M. Verduyn Lunel, Introduction of the theory of functional differential equations, Applied Mathematical Sciences, vol. 99, Springer, New York, 1991.
9. Hamori J. Rosks T. The use of CNN models in the subcortical visual pathway IEEE Trans. Circuits Systems 40 1993 182-194
10. Joy M.P. On the global convergence of a class of functional differential equations with applications in neural network theory J. Math. Anal. Appl. 232 1999 61-81
11. Joy M.P. Results concerning the absolute stability of delayed neural networks Neural Networks 13 2000 613-616
12. Kolmanovski V.B. Torelli L. Vermiglio R. Stability of some test equations with delay SIAM J. Math. Anal. 25 1994 948-961
13. Liao X.F. Wong K.W. Leung C.S. Wu Z.F. Hopf bifurcation and chaos in a single delayed neuron equation with non-monotonic activation function Chaos Solitons Fractals 12 2001 1535-1547
14. Liao X.F. Wong K.W. Wu Z.F. Bifurcation analysis on a two-neuron system with distributed delays Physica D 140 2001 123-141
15. Liao X.F. Wong K.W. Wu Z.F. Chen G. Novel robust stability criteria for interval delayed Hopfield neural networks IEEE Trans. Circuits Systems-I 48 11 2001 1355-1359
16. Liao X.F. Wong K.W. Yu J.B. Novel stability conditions for cellular neural networks with time delay Int. J. Bifurcat. Chaos. 11 7 2001 1853-1864
17. Liao X.F. Wu Z.F. Yu J.B. Stability analyses for cellular neural networks with continuous delay J. Comput. Appl. Math. 143 2002 29-47
18. Liao X.F. Yu J.B. Robust stability for interval Hopfield neural networks with time delays IEEE Trans. Neural Networks 9 1998 1042-1046
19. Liao X.F. Yu J.B. Qualitative analysis of bidirectional associative memory networks with time delays Int. J. Circuit Theory Appl. 26 1998 219-229
20. Liao X.F. Yu J.B. Chen G. Novel stability criteria for bidirectional associative memory with time delays Int. J. Circuit Theory Appl. 30 2002 519-546
21. Marcus C.M. Westervelt R.M. Stability of analogy neural networks with delay Phys. Rev. A 39 2 1989 347-359
22. Mohamad S. Gopalsamy K. Dynamics of a class of discrete-time neural networks and their continuous-time counterparts Math. Comput. Simulation 53 2000 1-39
23. Morita M. Associative memory with non-monotone dynamics Neural Networks 6 1993 115-126
24. Roska T. Wu C.W. Balsi M. Chua L.O. Stability and dynamics of delay-type general neural networks IEEE Trans. Circuits Systems-I 39 1992 487-490
25. Roska T. Wu C.W. Chua L.O. Stability of cellular neural network with dominant nonlinear and delay-type templates IEEE Trans. Circuits Systems-I 40 1993 270-272
26. Sree Hari Rao V. R. M. Phaneendra Bh. Global dynamics of bi-directional associative memory neural networks involving transmission delays and dead zones Neural Networks 12 1999 455-465
27. Tank D.W. Hopfield J.J. Neural computation by concentrating information in time Proc. Nat. Acad. Sci. USA 84 1987 1896-1991
28. Van den Driessche P. Zou X. Global attractivity in delayed Hopfield neural networks model SIAM J. Appl. Math. 58 1998 1878-1890
29. Yoshizawa S. Morita M. Amari S. Capacity of associate memory using a nonmonotonic neuron model Neural Networks 6 1993 167-176
30. Zhao H.Y. Global stability of bi-directional associative memory neural networks with distributed delays Phys. Lett. A 297 2002 182-190