Search Results - "Kristiansen, Kristian Uldall"

Geometric singular perturbation analysis of a dynamical target mediated drug disposition model by Kristiansen, Kristian Uldall

“…In this paper we present a mathematical analysis of a pharmacological ODE model for target mediated drug disposition (TMDD). It is known that solutions of this…”
Get full text

Slow divergence integral in regularized piecewise smooth systems by Huzak, Renato, Kristiansen, Kristian Uldall, Radunovic, Goran

“…In this paper we define the notion of slow divergence integral along sliding segments in regularized planar piecewise smooth systems. The boundary of such…”
Get full text

Bifurcations of mixed-mode oscillations in three-timescale systems: an extended prototypical example by Kaklamanos, Panagiotis, Popović, Nikola, Kristiansen, Kristian Uldall

“…We study a class of multi-parameter three-dimensional systems of ordinary differential equations that exhibit dynamics on three distinct timescales. We apply…”
Get full text

Singularly Perturbed Boundary-Equilibrium Bifurcations by Jelbart, Samuel, Kristiansen, Kristian Uldall, Wechselberger, Martin

“…Boundary equilibria bifurcation (BEB) arises in piecewise-smooth systems when an equilibrium collides with a discontinuity set under parameter variation…”
Get full text

Singularly perturbed boundary-focus bifurcations by Jelbart, Samuel, Kristiansen, Kristian Uldall, Wechselberger, Martin

“…We consider smooth systems limiting as ϵ→0 to piecewise-smooth (PWS) systems with a boundary-focus (BF) bifurcation. After deriving a suitable local normal…”
Get full text

Sliding Cycles of Regularized Piecewise Linear Visible–Invisible Twofolds by Huzak, Renato, Kristiansen, Kristian Uldall

“…The goal of this paper is to study the number of sliding limit cycles of regularized piecewise linear visible–invisible twofolds using the notion of slow…”
Get full text

Singular limit analysis of a model for earthquake faulting by Bossolini, Elena, Brøns, Morten, Kristiansen, Kristian Uldall

“…In this paper we consider the one dimensional spring-block model describing earthquake faulting. By using geometric singular perturbation theory and the…”
Get full text

Improved Gevrey-1 estimates of formal series expansions of center manifolds by Kristiansen, Kristian Uldall

“…In this paper, we show that the coefficients $\phi_n$ of the formal series expansions $y=\sum_{n=1}^\infty \phi_n x^n\in x\mathbb C[[x]]$ of center manifolds…”
Get full text

Revisiting the Kepler problem with linear drag using the blowup method and normal form theory by Kristiansen, Kristian Uldall

“…In this paper, we revisit the Kepler problem with linear drag. With dissipation, the energy and the angular momentum are both decreasing, but in…”
Get full text

Analytic weak-stable manifolds in unfoldings of saddle-nodes by Kristiansen, Kristian Uldall, Szmolyan, Peter

“…Any attracting, hyperbolic and proper node of a two-dimensional analytic vector-field has a unique strong-stable manifold. This manifold is analytic. The…”
Get full text

The dud canard: Existence of strong canard cycles in $\mathbb R^3 by Kristiansen, Kristian Uldall

“…In this paper, we provide a rigorous description of the birth of canard limit cycles in slow-fast systems in $\mathbb R^3$ through the folded saddle-node of…”
Get full text

Circularization in the damped Kepler problem by Kristiansen, Kristian Uldall, Ortega, Rafael

“…In this paper, we revisit the damped Kepler problem within a general family of nonlinear damping forces with magnitude $\delta \vert u\vert^{\beta}\vert \dot…”
Get full text

Sliding cycles of the regularized piecewise linear $VI_3$ two-fold by Huzak, Renato, Kristiansen, Kristian Uldall

“…The goal of this paper is to study the number of sliding limit cycles of a regularized piecewise linear $VI_3$ two-fold using the notion of slow divergence…”
Get full text

Blowup analysis of a hysteresis model based upon singular perturbations by Kristiansen, Kristian Uldall

“…In this paper, we provide a geometric analysis of a new hysteresis model that is based upon singular perturbations. Here hysteresis refers to a type of…”
Get full text

On $k$-summable normal forms of vector fields with one zero eigenvalue by De Maesschalck, Peter, Kristiansen, Kristian Uldall

“…In this paper, we study normal forms of analytic saddle-nodes in $\mathbb C^n$ with any Poincar\'e rank $k\in \mathbb N$. The approach and the results…”
Get full text

Travelling Waves and Exponential Nonlinearities in the Zeldovich-Frank-Kamenetskii Equation by Jelbart, Samuel, Kristiansen, Kristian Uldall, Szmolyan, Peter

“…We prove the existence of a family of travelling wave solutions in a variant of the $\textit{Zeldovich-Frank-Kamenetskii (ZFK) equation}$, a reaction-diffusion…”
Get full text

A stiction oscillator under slowly varying forcing: Uncovering small scale phenomena using blowup by Kristiansen, Kristian Uldall

“…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…”
Get full text

Slow divergence integral in regularized piecewise smooth systems by Huzak, Renato, Kristiansen, Kristian Uldall, Radunović, Goran

“…In this paper we define the notion of slow divergence integral along sliding segments in regularized planar piecewise smooth systems. The boundary of such…”
Get full text

On the pitchfork bifurcation of the folded node and other unbounded time-reversible connection problems in $\mathbb R^3 by Kristiansen, Kristian Uldall

“…In this paper, we revisit the folded node and the bifurcations of secondary canards at resonances $\mu\in \mathbb N$. In particular, we prove for the first…”
Get full text

The regularized visible fold revisited by Kristiansen, Kristian Uldall

“…The planar visible fold is a simple singularity in piecewise smooth systems. In this paper, we consider singularly perturbed systems that limit to this…”
Get full text