Convergence dynamics of delayed hopfield-type neural networks under almost periodic stimuli

Acta Applicandae Mathematicae

Volumn 76, Issue 2, 2003, Pages 117-135

  Mohamad, Sannay ^a  

^a UNIVERSITI BRUNEI DARUSSALAM   (Brunei Darussalam)

Author keywords

Almost periodic solutions; Exponential stability; Halanay inequalities; Hopfield type neural networks

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; LEARNING SYSTEMS; MATHEMATICAL MODELS; SYSTEM STABILITY; THEOREM PROVING;

EXPONENTIAL STABILITY;

NEURAL NETWORKS;

EID: 0037391616     PISSN: 01678019     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022919917909     Document Type: Article

References (33)

1. Baker, C. T. H. and Tang, A.: Generalized Halanay inequalities for Volterra functional differential equations and discretized versions, In: C. Corduneanu and I. W. Sandberg (eds), Volterra Equations and Applications (Arlington, TX, 1996), Stability Control Theory Methods Appl. 10, Gordon and Breach, Amsterdam, 2000, pp. 39-55.
2. Besicovitch, A. S.: Almost Periodic Functions, Dover, New York, 1954.
3. Cooke, R. L.: Almost periodic functions, Amer. Math. Monthly 88 (1981), 515-526.
4. Corduneanu, C.: Almost Periodic Functions, Interscience Publ., New York, 1968.
5. van den Driessche, P. and Zou, X.: Global attractivity in delayed Hopfield neural network models, SIAM J. Appl. Math. 58 (1998), 1878-1890.
6. Eckhorn, R., Bauer, R., Jordan, W., Brosch, M., Kruse, W., Munk, M. and Reitboeck, H. J.: Coherent oscillations: A mechanism for feature linking in the visual cortex, Biol. Cybern. 60 (1988), 121-130.
7. Eckhorn, R., Reitboeck, H. J., Arndt, M. and Dicke, P.: Linking via synchronization among distributed assemblies: Simulations of results from cat visual cortex, Neural Comput. 2 (1990), 293-307.
8. Engel, A. K., Kreiter, A. K., König, P. and Singer, W.: Synchronization of oscillatory neural responses between striate and extrastriate visual cortical areas of the cat, Proc. Natl. Acad. Sci. 88 (1991), 6048-6052.
9. Fang, Y. and Kincaid, G.: Stability analysis of dynamical neural networks, IEEE Trans. Neural Networks 7 (1996), 996-1006.
10. Fink, A. M.: Almost Periodic Differential Equations, Springer-Verlag, New York, 1974.
11. Forti, M., Manetti, S. and Marini, M.: A condition for global convergence of a class of symmetric neural circuits, IEEE Trans. Circuits Syst. 39 (1992), 480-483.
12. Forti, M., Manetti, S. and Marini, M.: Necessary and sufficient condition for absolute stability of neural networks, IEEE Trans. Circuits Syst. 41 (1994), 491-494.
13. Freeman, W. J. and Dijk, B. W.: Spatial patterns of visual cortical fast EEG during conditioned reflex in a rhesus monkey, Brain Res. 422 (1987), 267-276.
14. Gopalsamy, K.: Stability and Oscillations in Delay Differential Equations of Population Dynamics, Kluwer Acad. Publ., Dordrecht, 1992.
15. Gopalsamy, K. and He, X. Z.: Stability in asymmetric Hopfield nets with transmission delays, Physica D 76 (1994), 344-358.
16. Gray, C. M., König, P., Engel, A. K. and Singer, W.: Oscillatory responses in cat visual cortex exhibit intercolumnar synchronization which reflects global stimulus properties, Nature 388 (1989), 334-337.
17. Halanay, A.: Differential Equations, Academic Press, New York, 1966.
18. Haykin, S.: Neural Networks. A Comprehensive Foundation, 2nd edn, Prentice-Hall, New Jersey, 1999.
19. Hirsch, M. W.: Convergent activation dynamics in continuous time networks, Neural Networks 2 (1989), 331-349.
20. Hopfield, J. J.: Neurons with graded response have collective computational properties like those of two-state neurons, Proc. Natl. Acad. Sci. USA 81 (1984), 3088-3092.
21. Kelly, D. G.: Stability in contractive nonlinear neural networks, IEEE Trans. Biomed. Eng. 37 (1990), 231-242.
22. Kopell, N.: We got rhythm: Dynamical systems of the nervous system, Notices Amer. Math. Soc. 47 (2000), 6-16.
23. König, P. and Schillen, J. B.: Stimulus-dependent assembly formation of oscillatory responses: I. Synchronization, Neural Comput 3 (1991), 155-166.
24. LaSalle, L. P. and Lefschetz, S.: Stability by Lyapunov's Direct Method with Applications, Academic Press, New York, 1961.
25. Marcus, C. M. and Westervelt, R. M.: Stability of analog neural networks with delay, Phys. Rev. A 39 (1989), 347-359.
26. Matsuoka, K.: Stability conditions for nonlinear continuous neural networks with asymmetric connection weights, Neural Networks 5 (1992), 495-500.
27. Mohamad, S. and Gopalsamy, K.: Continuous and discrete Halanay-type inequalities, Bull. Austral. Math. Soc. 61 (2000), 371-385.
28. Yang, H. and Dillon, T. S.: Exponential stability and oscillation of Hopfield graded response neural networks, IEEE Trans. Neural Networks 5 (1994), 719-729.
29. Ye, H., Michel, A. N. and Wang, K.: Global stability and local stability of Hopfield neural networks with delays, Phys. Rev. E 50 (1994), 4206-4213.
30. Yi, Z.: Global exponential stability and periodic solutions of delay Hopfield neural networks, Internat. J. Systems Sci. 27 (1996), 227-231.
31. Yi, Z., Zhong, S. M. and Li, Z. L.: Periodic solutions and stability of Hopfield neural networks with variable delays, Internat. J. Systems Sci. 27 (1996), 895-901.
32. Yoshizawa, T.: Extreme stability and almost periodic solutions of functional-differential equations, Arch. Rat. Mech. Anal. 17 (1964), 148-170.
33. Yoshizawa, T.: Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions, Springer-Verlag, New York, 1975.