2 citations · 2 across the 6 of their papers we have counts for
11 papers
The Geometry of the Painlevé paradox
Noah Cheesman, S. John Hogan, Kristian Uldall Kristiansen
Painlevé showed that there can be inconsistency and indeterminacy in solutions to the equations of motion of a 2D rigid body moving on a sufficiently rough surface. The study of Pa…
Regularisation of isolated codimension-2 discontinuity sets
Noah Cheesman, Kristian Uldall Kristiansen, S. J. Hogan
Work on standard piecewise-smooth (PWS) dynamical systems, with codimension-1 discontinuity sets, relies on the Filippov framework, which does not always readily generalise to syst…
Singularly Perturbed Boundary-Equilibrium Bifurcations
Samuel Jelbart, Kristian Uldall Kristiansen, Martin Wechselberger
Boundary equilibria bifurcation (BEB) arises in piecewise-smooth systems when an equilibrium collides with a discontinuity set under parameter variation. Singularly perturbed BEB r…
A stiction oscillator under slowly varying forcing: Uncovering small scale phenomena using blowup
Kristian Uldall Kristiansen
In this paper, we consider a mass-spring-friction oscillator with the friction modelled by a regularized stiction model in the limit where the ratio of the natural spring frequency…
Singularly Perturbed Boundary-Focus Bifurcations
Samuel Jelbart, Kristian Uldall Kristiansen, Martin Wechselberger
We consider smooth systems limiting as to piecewise-smooth (PWS) systems with a boundary-focus (BF) bifurcation. After deriving a suitable local normal form, we study the…
On the pitchfork bifurcation of the folded node and other unbounded time-reversible connection problems in
Kristian Uldall Kristiansen
In this paper, we revisit the folded node and the bifurcations of secondary canards at resonances . In particular, we prove for the first time that pitchfork bifurc…