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

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December 2002, 1(4): 475-483. doi: 10.3934/cpaa.2002.1.475

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, Slovak Republic
2.	Department of Mathematics and Computer Science, University of Leicester, Leicester, LE1 7RH, United Kingdom

Received November 2001 Revised May 2002 Published September 2002

Abstract
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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.

Keywords: Periodic solutions, singular perturbations, bifurcations, travelling waves..

Mathematics Subject Classification: 34C23, 34C25, 34C37, 35B9.

Citation: Michal Fečkan, Vassilis Rothos. Bifurcations of periodics from homoclinics in singular O.D.E.: applications to discretizations of travelling waves of P.D.E.. Communications on Pure & Applied Analysis, 2002, 1 (4) : 475-483. doi: 10.3934/cpaa.2002.1.475

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