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Fitzhugh nagumo revisited: types of bifurcations, periodical forcing and stability regions by a lyapunov functional

Kostova, T and Ravindran, Renuka and Schonbek, Maria (2004) Fitzhugh nagumo revisited: types of bifurcations, periodical forcing and stability regions by a lyapunov functional. In: International Journal of Bifurcation and Chaos, 14 (3). pp. 913-925.

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Abstract

: We study several aspects of FitzHugh-Nagumo's (FH-N) equations without diffusion. Some global stability results as well as the boundedness of solutions are derived by using a suitably defined Lyapunov functional. We show the existence of both supercritical and subcritical Hopf bifurcations. We demonstrate that the number of all bifurcation diagrams is 8 but that the possible sequential occurrences of bifurcation events is much richer. We present a numerical study of all example exhibiting a series of various bifurcations, including subcritical Hopf bifurcations, homoclinic bifurcations and saddle-node bifurcations of equilibria and of periodic solutions. Finally, we study periodically forced FH-N equations. We prove that phase-locking occurs independently of the magnitude of the periodic forcing.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to World Scienti�c Publishing.
Keywords: FitzHugh{Nagumo;subcritical and supercritical Hopf bifurcation;homoclinic bifurcation;periodic forcing.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 19 Dec 2008 03:50
Last Modified: 19 Sep 2010 04:54
URI: http://eprints.iisc.ernet.in/id/eprint/16952

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