Abstract
It is well known that the slow divergence integral is a useful tool for obtaining a bound on the cyclicity of canard cycles in planar slow–fast systems. In this paper a new approach is introduced to determine upper bounds on the number of relaxation oscillations Hausdorff-close to a balanced canard cycle in planar slow–fast systems, by computing the box dimension of one orbit of a discrete one-dimensional dynamical system (so-called slow relation function) assigned to the canard cycle.
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I would like to thank Maja Resman for a number of useful comments.
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Huzak, R. Box Dimension and Cyclicity of Canard Cycles. Qual. Theory Dyn. Syst. 17, 475–493 (2018). https://doi.org/10.1007/s12346-017-0248-x
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DOI: https://doi.org/10.1007/s12346-017-0248-x