Revisiting the analysis of a codimension-three Takens–Bogdanov bifurcation in planar reversible systems

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

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Original languageEnglish
Pages (from-to)2567–2580
Journal / PublicationNonlinear Dynamics
Online published19 Apr 2019
Publication statusPublished - Jun 2019


A family of planar nilpotent reversible systems with an equilibrium point located at the origin has been studied in the recent paper Algaba et al. (Nonlinear Dyn 87:835–849, 2017). The authors investigate the candidate for an universal unfolding of a codimension-three degenerate case which exhibits a rich bifurcation scenario. However, a codimension-two point is missed in one of the two cases considered. In this paper, we complete the bifurcation set demonstrating the existence of this new organizing center and analyzing the dynamics generated in this case. Moreover, by means of the Melnikov theory, we study analytically four different global connections present in the system under consideration. Numerical continuation of the bifurcation curves illustrates that the first-order analytical approximation is valid in a large region of the parameter space.

Research Area(s)

  • 34C23, 37G10, 37G15, Global bifurcations, Melnikov function, Reversible systems, Takens–Bogdanov bifurcation