Bifurcation analysis of the travelling waveform of FitzHugh-Nagumo nerve conduction model equation

Chaos

Volumn 7, Issue 3, 1997, Pages 476-487

  Muruganandam, P ^a   Lakshmanan, M ^a  

^a BHARATHIDASAN UNIVERSITY   (India)

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EID: 3042871671     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.166219     Document Type: Article

References (33)

1. R. FitzHugh, Biophys. J. 1, 445 (1961).
2. R. FitzHugh, in Biological Engineering, edited by H. P. Schwan (McGraw-Hill, New York, 1969), pp. 1-85.
3. J. Nagumo, S. Arimoto, and S. Yoshizawa, Proc. IRE 50, 2061 (1962).
4. A. C. Scott, Rev. Mod. Phys. 47, 487 (1975).
5. A. C. Scott, Neurophysics (Wiley, New York, 1977), pp. 90-104.
6. A. T. Winfree, SIAM Rev. 32, 1 (1990).
7. T. Nagylaki, Genetics 83, 867 (1976).
8. S. Rajasekar and M. Lakshmanan, J. Theor. Biol. 133, 473 (1988).
9. S. Rajasekar and M. Lakshmanan, Physica D 32, 146 (1988).
10. S. Rajasekar and M. Lakshmanan, Int. J. Bifurcation Chaos 2, 201 (1992).
11. M. R. Guevara, L. Glass, M. C. Mackey, and A. Shrier, IEEE Trans. Syst. Man. Cybern. SMC-13, 790 (1983).
12. M. Feingold, D. L. Gonzalez, O. Piro, and H. Viturro, Phys. Rev. A 37, 4060 (1988).
13. S. Sato and X. S. Doi, Math. Biosci. 112, 243 (1992).
14. D. T. Kaplan, J. R. Clay, T. Manning, L. Glass, M. R. Guevara, and A. Shrier, Phys. Rev. Lett. 76, 4074 (1996).
15. M. Yamaguti, Proc. Jpn. Acad. 39, 726 (1963).
16. S. Yoshizawa and Y. Kitada, Math. Biosci. 5, 385 (1969).
17. P. Glendinning, in Chaos in Biological Systems, NATO ASI Life Sciences Series, edited by H. Degn, A. V Holden, and L. E. Olsen (Plenum, New York, 1987).
18. R. G. Caston, N. Cohen, and P. A. Lagerstrom, Q. Appl. Math. 32, 365 (1975).
19. S. P. Hastings, Q. J. Math. 27, 123 (1976).
20. G. A. Carpenter, J. Diff. Eqns. 23, 335 (1977).
21. S. T. Tu, SIAM J. Appl. Math. 49, 331 (1989).
22. H. Yamada and K. Nozaki, Prog. Theor. Phys. 84, 801 (1990).
23. M. Lakshmanan and K. Rajagopal, Phys. Lett. A 82, 266 (1981).
24. C. Kahlert and O. E. Rössler, Z. Naturforchung. 39a, 1200 (1984).
25. S. Rajasekar and M. Lakshmanan, J. Ther. Biol. 166, 275 (1994).
26. J. Rinzel, J. Math. Biol. 5, 363 (1978).
27. J. Rinzel and J. P. Keener, SIAM. J. Appl. Math. 43, 907 (1983).
28. M. -H. Chou, Comput. Math. Appl. 23, 85 (1992).
29. J. Guckenheimer and P. J. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Applied Mathematical Sciience Series (Springer, New York, 1983), Vol. 42.
30. J. Carr, Applications of Center Manifold Theory (Springer, New York, 1981).
31. J. D. Crawford, Rev. Mod. Phys. 63, 991 (1991).
32. G. Schmidt and A. Tondl, Nonlinear Vibrations (Cambridge University Press, Cambridge, 1986), pp. 82-86.
33. G. Matsumoto, K. Aihara, Y. Hanyu, N. Takahashi, S. Yosizawa, and J. Nagumo, Phys. Lett. A 123, 162 (1987).