LettersNo Access

ANALYTICAL DETERMINATION OF INITIAL CONDITIONS LEADING TO FIRING IN NERVE FIBERS

SABIR JACQUIR

Laboratoire LE2I, UMR CNRS 5158, Université de Bourgogne, 9 avenue Alain Savary, Dijon cedex, 21078, France

Search for more papers by this author

STEPHANE BINCZAK

Laboratoire LE2I, UMR CNRS 5158, Université de Bourgogne, 9 avenue Alain Savary, Dijon cedex, 21078, France

Search for more papers by this author

, and

JEAN-MARIE BILBAULT

Laboratoire LE2I, UMR CNRS 5158, Université de Bourgogne, 9 avenue Alain Savary, Dijon cedex, 21078, France

Search for more papers by this author

https://doi.org/10.1142/S0218127407019597Cited by:0 (Source: Crossref)

Abstract

An analytical solution characterizing initial conditions leading to action potential firing in smooth nerve fibers is determined, using the bistable equation. In the first place, we present a nontrivial stationary solution wave, then, using the perturbative method, we analyze the stability of this stationary wave. We show that it corresponds to a frontier between the initiation of the travelling waves and a decay to the resting state. Eventually, this analytical approach is extended to FitzHugh–Nagumo model.

Keywords:

References

J. Bell, Reaction–Diffusion Equations, eds. K. J. Brown and A. A. Lacey (1990) pp. 95–116. Crossref, Google Scholar
S. Binczak and J. M. Bilbault, Int. J. Bifurcation and Chaos 14, 1819 (2004). Link, Web of Science, Google Scholar
T. Bountis, C. F. Starmer and A. Bezerianos, Progr. Theoret. Phys. Suppl. 139, 12 (2000), DOI: 10.1143/PTPS.139.12. Crossref, Google Scholar
R. FitzHugh, Biophys. J. 1, 445 (1961). Crossref, Web of Science, Google Scholar
A. L. Hodgkin and A. F. Huxley, J. Physiol. 117, 500 (1952). Crossref, Web of Science, Google Scholar
J. P. Keener, J. Theor. Biol. 148, 49 (1991), DOI: 10.1016/S0022-5193(05)80465-5. Crossref, Web of Science, Google Scholar
T. J. Lewis and J. P. Keener, Siam J. Appl. Math. 61, 293 (2000). Crossref, Web of Science, Google Scholar
J. Nagumo, S. Arimoto and S. Yoshizawa, Proc. IRE 50, 2061 (1962), DOI: 10.1109/JRPROC.1962.288235. Crossref, Google Scholar
J. C. Neu, R. S. Preissig and W. Krassowska, Physica D 102, 285 (1997), DOI: 10.1016/S0167-2789(96)00203-5. Crossref, Web of Science, Google Scholar
A. Prat and Y. X. Li, Physica D 186, 50 (2003), DOI: 10.1016/S0167-2789(03)00236-7. Crossref, Web of Science, Google Scholar
A. C. Scott , Nonlinear Science ( Oxford University Press , NY , 1999 ) . Google Scholar
D. Terman, J. Diff. Eqs. 47, 406 (1983), DOI: 10.1016/0022-0396(83)90043-8. Crossref, Web of Science, Google Scholar