High-Order Analysis of Global Bifurcations in a Codimension-Three Takens-Bogdanov Singularity in Reversible Systems

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

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Detail(s)

Original languageEnglish
Article number2050017
Journal / PublicationInternational Journal of Bifurcation and Chaos
Volume30
Issue number1
Publication statusPublished - Jan 2020

Abstract

A codimension-three Takens-Bogdanov bifurcation in reversible systems has been very recently analyzed in the literature. In this paper, we study with the help of the nonlinear time transformation method, the codimension-one and -two homoclinic and heteroclinic connections present in the corresponding unfolding. The algorithm developed allows to obtain high-order approximations for the global connections, in such a way that it supplies in a very efficient manner the coefficients that would be obtained with high-order Melnikov functions. As we show, all our analytical predictions have excellent agreement with the numerical results. In particular we remark that, for the two different codimension-two points, the theoretical approximation coincides in six decimal digits with the numerical continuation, even being quite far from the codimension-three point. The better approximations we provide in this work will help in the study of reversible systems that exhibit this codimension-three Takens-Bogdanov bifurcation.

Research Area(s)

  • global connection, nonlinear time transformation, perturbation method, reversible system, Takens-Bogdanov bifurcation

Citation Format(s)

High-Order Analysis of Global Bifurcations in a Codimension-Three Takens-Bogdanov Singularity in Reversible Systems. / Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J.

In: International Journal of Bifurcation and Chaos, Vol. 30, No. 1, 2050017, 01.2020.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal