7 citations · 10 across the 6 of their papers we have counts for
6 papers
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…
Numerical Periodic Normalization at Codim 1 Bifurcations of Limit Cycles in DDEs
M. M. Bosschaert, B. Lentjes, L. Spek +1
Recent work in [53, 54] by the authors on periodic center manifolds and normal forms for bifurcations of limit cycles in delay differential equations (DDEs) motivates the derivatio…
Periodic Normal Forms for Bifurcations of Limit Cycles in DDEs
B. Lentjes, L. Spek, M. M. Bosschaert +1
A recent work by the authors on the existence of a periodic smooth finite-dimensional center manifold near a nonhyperbolic cycle in delay differential equations motivates the deriv…
Periodic Center Manifolds for DDEs in the Light of Suns and Stars
B. Lentjes, L. Spek, M. M. Bosschaert +1
In this paper we prove the existence of a periodic smooth finite-dimensional center manifold near a nonhyperbolic cycle in classical delay differential equations by using the Lyapu…
Interplay between normal forms and center manifold reduction for homoclinic predictors near Bogdanov-Takens bifurcation
Maikel M. Bosschaert, Yuri A. Kuznetsov
This paper provides for the first time correct third-order homoclinic predictors in -dimensional ODEs near a generic Bogdanov-Takens bifurcation point. To achieve this, higher-o…
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…