Mode locking and Arnold tongues in integrate-and-fire neural oscillators

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 60, Issue 2, 1999, Pages 2086-2096

  Coombes, S ^a   Bressloff, P C ^a  

^a LOUGHBOROUGH UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ACTION POTENTIAL; BIOLOGICAL MODEL; COMPARATIVE STUDY; MEMBRANE POTENTIAL; NERVE CELL; NONLINEAR SYSTEM; OSCILLOMETRY; PHYSIOLOGY; PROCEDURES; STATISTICAL MODEL; STATISTICS AND NUMERICAL DATA; SYNAPSE; SYNAPTIC TRANSMISSION;

ACTION POTENTIALS; MEMBRANE POTENTIALS; MODELS, BIOLOGICAL; MODELS, STATISTICAL; NEURONS; NONLINEAR DYNAMICS; OSCILLOMETRY; SYNAPSES; SYNAPTIC TRANSMISSION;

EID: 0033180689     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.60.2086     Document Type: Article

References (32)

1. A. V. Holden, Biol. Cybern. 21, 1 (1976).
2. M. R. Guevara, A. Shrier, and L. Glass, Am. J. Physiol. 254, H1 (1988).
3. G. A. Petrillo and L. Glass, Am. J. Physiol. 236, R311 (1984).
4. R. L. Calabrese and E. de Schutter, Trends Neurosci. 15, 439 (1992).
5. R. S. Mackay and C. Tresser, Physica D 19, 206 (1986).
6. D. K. Campbell, R. Galeeva, C. Tresser, and D. J. Uherka, Chaos 6, 121 (1996).
7. S. Coombes, Phys. Lett. A 255, 49 (1999).
8. P. C. Bressloff and S. Coombes, Neural Comput. (to be published).
9. L. F. Abbott and T. B. Kepler, in Statistical Mechanics of Neural Networks, edited by L. Garrido, Lecture Notes in Physics, Vol. 368 (Springer-Verlag, Berlin, 1990), pp. 5–18.
10. T. Sauer, Phys. Rev. Lett. 72, 3811 (1994).
11. D. M. Racicot and A. Longtin, Physica D 104, 184 (1997).
12. K. Yoshino, T. Nomura, K. Pakdaman, and S. Sato, Phys. Rev. E 59, 956 (1999).
13. C. C. Chow, Physica D 118, 343 (1998).
14. D. T. Kaplan, J. R. Clay, T. Manning, L. Glass, M. R. Guevara, and A. Shrier, Phys. Rev. Lett. 76, 4074 (1996).
15. J. P. Keener, F. C. Hoppensteadt, and J. Rinzel, SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 41, 816 (1981).
16. S. Coombes and G. J. Lord, Phys. Rev. E 56, 5809 (1997).
17. P. C. Bressloff and S. Coombes, Int. J. Mod. Phys. B 11, 2343 (1997).
18. P. C. Bressloff and S. Coombes, Physica D 126, 99 (1999).
19. C. van Vreeswijk, L. F. Abbott, and G. B. Ermentrout, J. Comput. Neurosci. 1, 313 (1994).
20. G. B. Ermentrout, J. Math. Biol. 12, 327 (1981).
21. P. C. Bressloff and S. Coombes, Phys. Rev. Lett. 81, 2384 (1998).
22. P. C. Bressloff and S. Coombes, Phys. Rev. Lett. 81, 2168 (1998).
23. J. Keener and J. Sneyd, Mathematical Physiology (Springer, New York, 1998).
24. F. C. Hoppensteadt and E. M. Izhikevich, Weakly Connected Neural Networks, Applied Mathematical Sciences Vol. 126 (Springer-Verlag, Berlin, 1997).
25. Z. Mainen and T. J. Sejnowski, Science 268, 1503 (1995).
26. R. R. D. van Steveninck, G. D. Lewen, S. P. Strong, R. Koberle, and W. Bialek, Science 275, 1805 (1997).
27. J. D. Hunter, J. G. Milton, P. J. Thomas, and J. D. Cowan, J. Neurophysiol. 80, 1427 (1998).
28. A. M. Thomson and J. Deuchars, Trends Neurosci. 17, 119 (1994).
29. M. V. Tsodyks and H. Markram, Proc. Natl. Acad. Sci. USA 94, 719 (1997).
30. L. F. Abbott, J. A. Varela, K. Sen, and S. B. Nelson, Science 275, 220 (1997).
31. L. F. Abbott and E. Marder, in Methods in Neuronal Modelling, 2nd ed., edited by C. Kock and I. Segev (MIT Press, Cambridge, MA, 1989), pp. 135–169.
32. A. Longtin and D. R. Chialvo, Phys. Rev. Lett. 81, 4012 (1998).