Canard explosion in chemical and optical systems

Elena Shchepakina; Olga Korotkova

doi:10.3934/dcdsb.2013.18.495

Article Contents

2013, Volume 18, Issue 2: 495-512. Doi: 10.3934/dcdsb.2013.18.495

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Canard explosion in chemical and optical systems

Elena Shchepakina^1, and
Olga Korotkova^2,

1.
Department of Technical Cybernetics, Samara State Aerospace University, Molodogvardeiskaya 151, Samara 443001
2.
Department of Physics, University of Miami, 1320 Campo Sano Drive, Coral Gables, FL 33146

Received: September 30, 2011

Revised: March 31, 2012

Published: February 2013

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Abstract

The paper deals with the study of the relation between the Andronov--Hopf bifurcation, the canard explosion and the critical phenomena for the van der Pol's type system of singularly perturbed differential equations. Sufficient conditions for the limit cycle birth bifurcation in the case of the singularly perturbed systems are investigated. We use the method of integral manifolds and canards techniques to obtain the conditions under which the system possesses the canard cycle. Through the application to some chemical and optical models it is shown that the canard point should be considered as the critical value of the control parameter.

Keywords:

Mathematics Subject Classification: 34C45, 34E15, 34E17, 37G10, 78A60, 80A30.

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