Qualitative analysis of a neural network model with multiple time delays

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 9, Issue 8, 1999, Pages 1585-1595

  Campbell, Sue Ann ^a   Ruan, Shigui ^b   Wei, Junjie ^c  

^a UNIVERSITY OF WATERLOO   (Canada)

^b DALHOUSIE UNIVERSITY   (Canada)

^c NORTHEAST NORMAL UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033177129     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127499001103     Document Type: Article

References (23)

1. Babcock, K. L. & Westervelt, R. M. [1987] "Dynamics of simple electronic neural networks," Physica D28, 305-316.
2. Baldi, P. & Atiya, A. F. [1994] "How delays affect neural dynamics and learning," IEEE Trans. Neural Networks 5, 612-621.
3. Bélair, J. [1993] "Stability in a model of a delayed neural network," J. Dyn. Diff. Eqs. 5, 607-623.
4. Bélair, J., Campbell, S. & van den Driessche, P. [1996] "Frustration, stability and delay-induced oscillations in a neural network model," SIAM J. Appl. Math. 56, 245-255.
5. Campbell, S. A. [1999] "Stability and bifurcation of a simple neural network with multiple time delays," Fields Inst. Commun. 21, 65-79.
6. Gopalsamy, K. & He, X.-Z. [1994] "Stability in asymmetric Hopfield networks with transmission delays," Physica D76, 344-358.
7. Gopalsamy, K. & Leung, I. [1996] "Delay induced periodicity in a neural network of excitation and inhibition," Physica D89, 395-426.
8. Hale, J. & Huang, W. [1993] "Global geometry of the stable regions for two delay differential equations," J. Math. Anal. Appl. 178, 344-362.
9. Hale, J. & Verduyn Lunel, S. M. [1993] Introduction to Functional Differential Equations (Springer-Verlag, NY).
10. Hopfield, J. [1984] "Neurons with graded response have collective computational properties like those of two-state neurons," Proc. Nat. Acad. Sci. USA 81, 3088-3092.
11. Kharitonov, V. L. & Paice, A. D. B. [1997] "Robust stability of a class of neural networks with time delays," J. Dyn. Diff. Eqs. 9, 67-91.
12. Liao, X. & Liao, Y. [1997] "Stability of Hopfield-type neural networks II," Sci. China Ser. A40, 813-816.
13. Majee, N. C. & Roy, A. B. [1997] "Temporal dynamics of a two-neuron continuous network model with time delay," Appl. Math. Modelling 21, 673-679.
14. Mallet-Paret, J. & Sell, G. R. [1996] "The Poincare-Bendixson theorem for monotone cyclic feedback systems with delay," J. Diff. Eqs. 125, 385-440.
15. Marcus, C. M., Waugh, F. R. & Westervelt, R. M. [1991] "Nonlinear dynamics and stability of analog neural networks," Physica D51, 234-247.
16. Marcus, C. M. & Westervelt, R. M. [1989] "Stability of analog neural network with delay," Phys. Rev. A39, 347-359.
17. Olien, L. &B élair, J. [1997] "Bifurcations, stability and monotonicity properties of a delayed neural network model," Physica D102, 349-363.
18. Ruan, S. & Wei, J. [1999] "On the zeros of transcendental functions with applications to stability of delay differential equations," preprint.
19. Shayer, L. P. & Campbell, S. A. [1999] "Stability, bifurcation and complex dynamics in a system of two coupled Hopfield neurons with multiple time delays," SIAM J. Appl. Math., to appear.
20. van den Driessche, P. & Zou, X. [1998] "Global attractivity in delayed Hopfield neural network models," SIAM J. Appl. Math. 58, 1878-1890.
21. Wei, J. & Ruan, S. [1999] "Stability and bifurcation in a neural network model with two delays," Physica D130, 255-272.
22. Ye, H., Michel, A. N. & Wang, K. [1994] "Global stability and local stability of Hopfield neural networks with delays," Phys. Rev. E50, 4206-4213.
23. Ye, H., Michel, A. N. & Wang, K. [1995] "Qualitative analysis of Cohen-Grossberg neural networks with multiple delays," Phys. Rev. E51, 2611-2618.