# American Institute of Mathematical Sciences

July  2013, 33(7): 3085-3108. doi: 10.3934/dcds.2013.33.3085

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

 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  January 2013

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.
Citation: Jianhe Shen, Maoan Han. Bifurcations of canard limit cycles in several singularly perturbed generalized polynomial Liénard systems. Discrete & Continuous Dynamical Systems, 2013, 33 (7) : 3085-3108. doi: 10.3934/dcds.2013.33.3085
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