422 citations · 2.4k across the 156 of their papers we have counts for
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Traveling waves for a bistable equation with nonlocal-diffusion
Franz Achleitner, Christian Kuehn
We consider a single component reaction-diffusion equation in one dimension with bistable nonlinearity and a nonlocal space-fractional diffusion operator of Riesz-Feller type. Our…
From random Poincaré maps to stochastic mixed-mode-oscillation patterns
Nils Berglund, Barbara Gentz, Christian Kuehn
We quantify the effect of Gaussian white noise on fast--slow dynamical systems with one fast and two slow variables, which display mixed-mode oscillations owing to the presence of…
Critical Transitions in Social Network Activity
Christian Kuehn, Erik A. Martens, Daniel Romero
A large variety of complex systems in ecology, climate science, biomedicine and engineering have been observed to exhibit tipping points, where the internal dynamical state of the…
On Bounded Positive Stationary Solutions for a Nonlocal Fisher-KPP Equation
Franz Achleitner, Christian Kuehn
We study the existence of stationary solutions for a nonlocal version of the Fisher-Kolmogorov-Petrovskii-Piscounov (FKPP) equation. The main motivation is a recent study by Berest…
Large Deviations for Nonlocal Stochastic Neural Fields
Christian Kuehn, Martin G. Riedler
We study the effect of additive noise on integro-differential neural field equations. In particular, we analyze an Amari-type model driven by a -Wiener process and focus on nois…