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20192025
most citedInterplay between normal forms and center manifold reduction for homoclinic predictors near Bogdanov-Takens bifurcation

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math.DS2025

Bifurcation Analysis of Generalized Hopf Bifurcation in Ordinary and Delay Differential Equations

N. A. M. Delmeire, M. M. Bosschaert, Yu. A. Kuznetsov

The generalized Hopf (Bautin) bifurcation is a well-studied codimension two bifurcation characterized by an equilibrium with a pair of simple purely imaginary eigenvalues as the on…

math.DS2019

Switching to nonhyperbolic cycles from codimension two bifurcations of equilibria of delay differential equations

Maikel M. Bosschaert, Sebastiaan G. Janssens, Yuri A. Kuznetsov

In this paper we perform the parameter-dependent center manifold reduction near the generalized Hopf (Bautin), fold-Hopf, Hopf-Hopf and transcritical-Hopf bifurcations in delay dif…