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Extending slow manifold near generic transcritical canard point

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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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Authors and Affiliations

  1. School of Economics and Management, Shanghai Institute of Technology, Shanghai, 201418, China

    Hai-bo Lu

  2. Department of Mathematics, East China Normal University, Shanghai, 200241, China

    Ming-kang Ni

  3. School of Mathmatics and Information Science and Technology, Hebei Normal University of Science and Technology, Hebei, 066004, China

    Li-meng Wu

Authors
  1. Hai-bo Lu
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  2. Ming-kang Ni
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  3. Li-meng Wu
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Correspondence to Hai-bo Lu.

Additional information

Supported by the National Natural Science Foundation of China (No. 71501130), Natural Science Foundation of Hebei Province (A2015407063).

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Lu, Hb., Ni, Mk. & Wu, Lm. Extending slow manifold near generic transcritical canard point. Acta Math. Appl. Sin. Engl. Ser. 33, 989–1000 (2017). https://doi.org/10.1007/s10255-017-0713-y

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  • DOI: https://doi.org/10.1007/s10255-017-0713-y

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