10 papers
A geometric approach to inner problems associated with exponentially small splitting phenomena in local bifurcations
Kristian Uldall Kristiansen
In this paper, we study analytic nonlinear partial differential equations for of the form $x^2 \mathbf y'_x(1+\mathcal O(x)) + \mathbf y'…
A geometric approach to exponentially small splitting: The generic zero-Hopf bifurcation of co-dimension two
Kristian Uldall Kristiansen
In this paper, we consider the unfolding of the real-analytic and generic zero-Hopf bifurcation of co-dimension two. It is well-known that in an open set of parameter space the spl…
A geometric approach to exponentially small splitting: Zero-Hopf bifurcations of arbitrary co-dimension
Kristian Uldall Kristiansen
In this paper, we present a geometric approach to exponentially small splitting in zero-Hopf bifurcations of arbitrary co-dimension. In further details, we consider a family of pro…
On -summable normal forms of vector fields with one zero eigenvalue
Peter De Maesschalck, Kristian Uldall Kristiansen
In this paper, we study normal forms of analytic saddle-nodes in with any Poincaré rank . The approach and the results generalize those of Boncka…
Switching, Multiple Time-Scales and Geometric Blow-Up in a Low-Dimensional Gene Regulatory Network
Samuel Jelbart, Kristian Uldall Kristiansen, Peter Szmolyan
ODE-based models for gene regulatory networks (GRNs) can often be formulated as smooth singular perturbation problems with multiple small parameters, some of which are related to t…
On entry-exit formulas for degenerate turning point problems in planar slow-fast systems
Renato Huzak, Kristian Uldall Kristiansen
In this paper, we study degenerate entry-exit problems associated with planar slow-fast systems having an invariant line with a turning point at . The dege…