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

^*此作品的通讯作者

数学科学学院

Shanghai Institute of Technology
Hebei Normal University of Science and Technology

科研成果: 期刊稿件 › 文章 › 同行评审

7 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	989-1000
页数	12
期刊	Acta Mathematicae Applicatae Sinica
卷	33
期	4
DOI	https://doi.org/10.1007/s10255-017-0713-y
出版状态	已出版 - 1 10月 2017

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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.",

keywords = "blow-up technique, canards, singular perturbation, transcritical bifurcation",

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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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