422 citations · 2.4k across the 156 of their papers we have counts for
8 papers · 1 filter
Heterogeneous Population Dynamics and Scaling Laws near Epidemic Outbreaks
Andreas Widder, Christian Kuehn
In this paper, we focus on the influence of heterogeneity and stochasticity of the population on the dynamical structure of a basic susceptible-infected-susceptible (SIS) model. Fi…
Numerical Continuation and SPDE Stability for the 2D Cubic-Quintic Allen-Cahn Equation
Christian Kuehn
We study the Allen-Cahn equation with a cubic-quintic nonlinear term and a stochastic -trace-class stochastic forcing in two spatial dimensions. This stochastic partial differen…
Efficient Gluing of Numerical Continuation and a Multiple Solution Method for Elliptic PDEs
Christian Kuehn
Numerical continuation calculations for ordinary differential equations (ODEs) are, by now, an established tool for bifurcation analysis in dynamical systems theory as well as acro…
Analysis and numerics of traveling waves for asymmetric fractional reaction-diffusion equations
Franz Achleitner, Christian Kuehn
We consider a scalar reaction-diffusion equation in one spatial dimension with bistable nonlinearity and a nonlocal space-fractional diffusion operator of Riesz-Feller type. We pre…
A Remark on Geometric Desingularization of a Non-Hyperbolic Point using Hyperbolic Space
Christian Kuehn
A steady state (or equilibrium point) of a dynamical system is hyperbolic if the Jacobian at the steady state has no eigenvalues with zero real parts. In this case, the linearized…
Early-Warning Signs for Pattern-Formation in Stochastic Partial Differential Equations
Karna Gowda, Christian Kuehn
There have been significant recent advances in our understanding of the potential use and limitations of early-warning signs for predicting drastic changes, so called critical tran…