Hopf bifurcation in bidirectional associative memory neural networks with delays: Analysis and computation

Journal of Computational and Applied Mathematics

Volumn 167, Issue 1, 2004, Pages 73-90

  Wang, Lin ^a   Zou, Xingfu ^a  

^a MEMORIAL UNIVERSITY OF NEWFOUNDLAND   (Canada)

Author keywords

Bidirectional associative memory; Delay; Hopf bifurcation; Liapunov functional; Neural networks; Stability

Indexed keywords

ALGORITHMS; BIFURCATION (MATHEMATICS); CONVERGENCE OF NUMERICAL METHODS;

GLOBAL STABILITY; HOPF BIFURCATION;

NEURAL NETWORKS;

MATHEMATICAL ANALYSIS;

EID: 2342442918     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2003.09.047     Document Type: Article

References (28)

1. Bélair J. Stability in a model of a delayed neural network J. Dyn. Differential Equations 5 1993 607-623
2. Campbell S.A. Ruan S. Wei J. Qualitative analysis of a neural network model with multiple time delays Internat. J. Bifur. Chaos Appl. Sci. Eng. 9 8 1999 1585-1595
3. Cao Y. Wu Q. A note on stability of analog neural networks with time delays IEEE Trans. Neural Networks 7 1996 1533-1535
4. Cooke K. van den Driessche P. On zeros of some transcendental equation Funkcial. Ekvac. 29 1985 77-90
5. Deimling K. Nonlinear Functional Analysis 1985 Springer New York
6. Feng C. Plamondon R. On the stability analysis of delayed neural networks systems Neural Networks 14 2000 1181-1188
7. Fielder M. Special Matrices and their Applications in Numerical Mathematics 1986 Martinus Nijhoff Publishers Boston
8. Forti M. On global asymptotic stability of a class of nonlinear systems arising in neural network theory J. Differential Equations 113 1994 246-264
9. Gopalsamy K. He X. Delay-independent stability in bidirectional associative memory networks IEEE Trans. Neural Networks 5 1994 998-1002
10. Gopalsamy K. He X. Stability in asymmetric Hopfield nets with transmission delays Phys. D 76 1994 344-358
11. Guan Z. Chen G. Qin Y. On equilibria, stability, and instability of Hopfield neural networks IEEE Trans. Neural Networks 2 2000 534-540
12. Hassard B.D. Kazavinoff N.D. Wan Y.H. Theory and Applications of the Hopf Bifurcation 1981 Cambridge University Press Cambridge, MA
13. Hopfield J. Neurons with graded response have collective computational properties like those of two-stage neurons Proc. Natl. Acad. Sci. USA 81 1984 3088-3092
14. Kazarinoff N.D. Wan Y.H. van den Driessche P. Hopf bifurcation and stability of periodic solutions of differential-difference and integro-differential equations J. Inst. Math. Appl. 21 1978 461-477
15. Kosko B. Adaptive bidirectional associative memories Appl. Opt. 26 1987 4947-4960
16. Kosko B. Bidirectional associative memories IEEE Trans. Systems Man Cybernet. 18 1988 49-60
17. Kosko B. Unsupervised learning in noise IEEE Trans. Neural Networks 1 1990 1-12
18. Lu H. On stability of nonlinear continuous-time neural networks with delays Neural Networks 13 2000 1135-1143
19. Marcus C. Westervelt R. Stability of analog neural networks with delay Phys. Rev. A 39 1989 347-359
20. Matsuoka K. Stability conditions for nonlinear continuous neural networks with asymmetric connection weights Neural Networks 5 1992 495-500
21. Mohamad S. Globaly exponential stability in continuous-time and discrete-time delayed bidirectional neural networks Physica D 159 2001 233-251
22. Shampine L.F. Thompson S. Solving DDEs in MATLAB Appl. Numer. Math. 37 2001 441-458
23. Shayer L.P. Campbell S.A. Stability, bifurcation, and multistability in a system of two coupled neurons with multiple time delays SIAM J. Appl. Math. 61 2 2000 673-700
24. Tank D. Hopfield J. Simple neural optimization networks: An A/D converter, signal decision circuit and a linear programming circuit IEEE Trans. Circuits Systems 33 1986 533-541
25. van den Driessche P. Zou X. Global attractivity in delayed Hopfield neural network models SIAM J. Appl. Math. 58 1998 1878-1890
26. Wei J. Ruan S. Stability and bifurcation in a neural network model with two delays Phys. D 130 1999 255-272
27. Wu J. Symmetric functional-differential equations and neural networks with memory Trans. Amer. Math. Soc. 350 1999 4799-4838
28. Wu J. Zou X. Patterns of sustained oscillations in neural networks with delayed iteractions Appl. Math. Comput. 73 1995 55-75