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Planar Canards with Transcritical Intersections

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Abstract

We review essential techniques in the study of families of periodic orbits of slow-fast systems in the plane. The techniques are demonstrated by treating orbits passing through unfoldings of transcritical intersections of curves of singular points in the most generic setting. We show that such transcritical intersections can generate canard type orbits. The stability of limit cycles of canard type containing that pass near transcritical intersections is examined by means of the slow divergence integral.

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Acknowledgements

The author thanks the anonymous reviewers for their many useful remarks and suggestions. The author acknowledges support from FWO Vlaanderen.

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  1. Hasselt University, Martelarenlaan 42, 3500, Hasselt, Belgium

    P. De Maesschalck

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De Maesschalck, P. Planar Canards with Transcritical Intersections. Acta Appl Math 137, 159–184 (2015). https://doi.org/10.1007/s10440-014-9994-9

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