A note on convergence under dynamical thresholds with delays

IEEE Transactions on Neural Networks

Volumn 9, Issue 1, 1998, Pages 231-233

  Pakdaman, K ^a,b   Malta, C P ^c  

^a OSAKA UNIVERSITY   (Japan)

^b INSERM   (France)

^c UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

Convergence; Delay; Dynamical threshold; Oscillation

Indexed keywords

ASYMPTOTIC STABILITY; CONVERGENCE OF NUMERICAL METHODS; MATHEMATICAL MODELS; OSCILLATIONS;

DYNAMIC THRESHOLD NEURON MODELS;

NEURAL NETWORKS;

EID: 0031675589     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/72.655047     Document Type: Article

References (18)

1. K. Gopalsamy and I. K. C. Leung, "Convergence under dynamical thresholds with delays," IEEE Trans. Neural Networks, vol. 8, pp. 341-348, 1997.
2. J. Mallet-Paret and G. R. Sell, "The Poincaré Bendixson theorem for monotone cyclic feedback systems with delay," J. Diff. Eq., vol. 125, pp. 441-489, 1996.
3. Y. Cao, "The discrete Lyapunov function for scalar differential delay equations," J. Diff. Eq., vol. 87, pp. 365-390, 1990.
4. O. Arino, "A note on 'the discrete Lyapunov function...'," J. Diff. Eq., vol. 104, pp. 169-181, 1993.
5. J. Mallet-Paret, "Morse decompositions for delay-differential equations," J. Diff. Eq., vol. 72, pp. 270-315, 1988.
6. B. Fiedler and J. Mallet-Paret, "Connections between Morse sets for delay differential equations," J. Reine Angew. Math., vol. 397, pp. 23-41, 1989.
7. C. McCord and K. Mischaikow, "On the global dynamics of attractors for scalar delay equations," J. Amer. Math. Soc., vol. 9, pp. 1095-1133, 1996.
8. K. Pakdaman, C. P. Malta, C. Grotta-Ragazzo, and J.-F. Vibert, "Effect of delay on the boundary of the basin of attraction in a self-excited single neuron," Neural Computa., vol. 9, pp. 319-336, 1997.
9. K. Pakdaman, C. P. Malta, C. Grotta-Ragazzo, O. Arino, and J.-F. Vibert, "Transient oscillations in continuous-time excitatory ring neural networks with delay," Phys. Rev. E, vol. 55, pp. 3234-3248, 1997.
10. H. L. Smith, Monotone Dynamical Systems an Introduction to the Theory of Competitive and Cooperative Systems, Mathematical Surveys and Monographs, vol. 41. Providence, RI: Amer. Math. Soc., 1995.
11. P. Takáč, "Domains of attraction of generic omega-limit sets for strongly monotone semiflows," Zeitsch. Anal. Anwend., vol. 10, pp. 275-317, 1991.
12. O. Arino and R. Benkhalti, "Periodic solutions for x = λf(x(t), x(t - 1))," in Proc. Roy. Soc. Edinburgh, 1988, vol. 109A, pp. 245-260.
13. A. F. Ivanov and A. N. Sharkovsky, "Oscillations in singularly perturbed delay equations," in Dynamics Reported 1, C. K. R. T. Jones, U. Kirchgraber, and H. O. Walther, Eds. New-York: Springer-Verlag, 1992, pp. 164-224.
14. A. N. Sharkovsky, Yu. L. Maistrenko, and E. Yu. Romanenko, Difference Equations and Their Applications. Dordrecht, The Netherlands: Kluwer, 1993.
15. K. Gopalsamy and X.-Z. He, "Stability in asymmetric Hopfield nets with transmission delays," Physica D, vol. 76, pp. 344-358, 1994.
16. T. Roska, C. W. Wu, M. Balsi, and L. O. Chua, "Stability and dynamics of delay-type general and cellular neural networks," IEEE Trans. Circuits Syst. I, vol. 39, pp. 487-490, 1992.
17. K. Pakdaman, C. P. Malta, C. Grotta-Ragazzo, and J.-F. Vibert, "Asymptotic behavior of irreducible excitatory networks of graded-response neurons," Publicações Universidade de São Paulo, IFUSP/P-1200, 1996.
18. J. Bélair, S. A. Campbell, and P. van den Driessche, "Frustation, stability and delay-induced oscillations in a neural network model," SIAM J. Appl. Math., vol. 56, pp. 245-255, 1996.