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Poincaré–Andronov–Hopf Bifurcation and the Local Hilbert’s 16th Problem

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Abstract

This survey on the Hopf bifurcation (in a broad sense) has been written in order to clarify some aspects in the light of recent progresses made in the local Hilbert’s 16th problem. As a practical guide, it can be of potential interest for applications. It includes dynamical and multi-scales versions.

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  1. Laboratoire Jacques-Louis Lions, UMR 7598 CNRS, Université P.-M. Curie, Paris 6, 4 Place Jussieu, 75252, Paris Cedex, France

    Jean-Pierre Françoise

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  1. Jean-Pierre Françoise
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Correspondence to Jean-Pierre Françoise.

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The author is partially supported by an ANR grant “Analyse non linéaire et applications aux rythmes du vivant” BLAN07-2-182920.

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Françoise, JP. Poincaré–Andronov–Hopf Bifurcation and the Local Hilbert’s 16th Problem. Qual. Theory Dyn. Syst. 11, 61–77 (2012). https://doi.org/10.1007/s12346-012-0071-3

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