Extending slow manifold near generic transcritical canard point

Hai bo Lu; Ming kang Ni; Li meng Wu

doi:10.1007/s10255-017-0713-y

Extending slow manifold near generic transcritical canard point

Hai bo Lu, Ming kang Ni, Li meng Wu

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We consider the dynamics of planar fast-slow systems near generic transcritical type canard point. By using geometric singular perturbation theory combined with the recently developed blow-up technique, the existence of canard cycles, relaxation oscillations and solutions near the attracting branch of the critical manifold is established. The asymptotic expansion of the parameter for which canard exists is obtained by a version of the Melnikov method.

Original language	English
Pages (from-to)	989-1000
Number of pages	12
Journal	Acta Mathematicae Applicatae Sinica
Volume	33
Issue number	4
DOIs	https://doi.org/10.1007/s10255-017-0713-y
State	Published - 1 Oct 2017

Keywords

blow-up technique
canards
singular perturbation
transcritical bifurcation

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abstract = "We consider the dynamics of planar fast-slow systems near generic transcritical type canard point. By using geometric singular perturbation theory combined with the recently developed blow-up technique, the existence of canard cycles, relaxation oscillations and solutions near the attracting branch of the critical manifold is established. The asymptotic expansion of the parameter for which canard exists is obtained by a version of the Melnikov method.",

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AU - Ni, Ming kang

AU - Wu, Li meng

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N2 - We consider the dynamics of planar fast-slow systems near generic transcritical type canard point. By using geometric singular perturbation theory combined with the recently developed blow-up technique, the existence of canard cycles, relaxation oscillations and solutions near the attracting branch of the critical manifold is established. The asymptotic expansion of the parameter for which canard exists is obtained by a version of the Melnikov method.

AB - We consider the dynamics of planar fast-slow systems near generic transcritical type canard point. By using geometric singular perturbation theory combined with the recently developed blow-up technique, the existence of canard cycles, relaxation oscillations and solutions near the attracting branch of the critical manifold is established. The asymptotic expansion of the parameter for which canard exists is obtained by a version of the Melnikov method.

KW - blow-up technique

KW - canards

KW - singular perturbation

KW - transcritical bifurcation

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Extending slow manifold near generic transcritical canard point

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Keywords

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