Bifurcations of periodics from homoclinics in singular O.D.E.: applications to discretizations of travelling waves of P.D.E.

Michal Fečkan; Vassilis Rothos

doi:10.3934/cpaa.2002.1.475

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2002, Volume 1, Issue 4: 475-483. Doi: 10.3934/cpaa.2002.1.475

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Bifurcations of periodics from homoclinics in singular O.D.E.: applications to discretizations of travelling waves of P.D.E.

Michal Fečkan^1, and
Vassilis Rothos^2,

1.
Department of Mathematical Analysis and Numerical Mathematics, Comenius University, Mlynská dolina, 842 48 Bratislava
2.
Department of Mathematics and Computer Science, University of Leicester, Leicester, LE1 7RH

Received: October 31, 2001

Revised: April 30, 2002

Published: November 2002

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Abstract

Bifurcations of periodic solutions from homoclinic ones are investigated for certain singularly perturbed systems of autonomous ordinary differential equations in $\mathbb R^4$. Results are applied to discretization of travelling waves of certain p.d.e.

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Mathematics Subject Classification: 34C23, 34C25, 34C37, 35B99.

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