Bifurcations of canard limit cycles in several singularly perturbedgeneralized polynomial Liénard systems

Jianhe Shen; Maoan Han

doi:10.3934/dcds.2013.33.3085

Article Contents

2013, Volume 33, Issue 7: 3085-3108. Doi: 10.3934/dcds.2013.33.3085

This issue Previous Article On the dichotomic behavior of discrete dynamical systems on the half-line Next Article On the stability of periodic orbits in delay equations with large delay

Bifurcations of canard limit cycles in several singularly perturbed generalized polynomial Liénard systems

Jianhe Shen^1, and
Maoan Han^2,

1.
School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, 350007
2.
Department of Mathematics, Shanghai Normal University, Shanghai 200234

Received: January 2012

Revised: November 2012

Published online: January 2013

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Abstract

This paper is concerned with bifurcations of canard limit cycles in several singularly perturbed generalized polynomial Liénard systems. By analyzing the multiplicities of the zeroes of the slow divergence integrals and their complete unfolding, the upper bounds of canard limit cycles bifurcating from the suitable limit periodic sets through respectively the generic Hopf breaking mechanism, the generic jump breaking mechanism and a succession of the Hopf and jump mechanisms in these polynomial Liénard systems are obtained.

Keywords:

Mathematics Subject Classification: 37G15, 34C07, 34E17.

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References

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