422 citations · 2.4k across the 156 of their papers we have counts for
10 papers · 2 filters
Mathematical Analysis of Nonlocal PDEs for Network Generation
Tobias Böhle, Christian Kuehn
In this paper, we study a certain class of nonlocal partial differential equations (PDEs). The equations arise from a key problem in network science, i.e., network generation from…
Controlling Canard Cycles
Hildeberto Jardon-Kojakhmetov, Christian Kuehn
Canard cycles are periodic orbits that appear as special solutions of fast-slow systems (or singularly perturbed Ordinary Differential Equations). It is well known that canard cycl…
A Random Dynamical Systems Perspective on Isochronicity for Stochastic Oscillations
Maximilian Engel, Christian Kuehn
For an attracting periodic orbit (limit cycle) of a deterministic dynamical system, one defines the isochron for each point of the orbit as the cross-section with fixed return time…
Discretized Fast-Slow Systems with Canards in Two Dimensions
Maximilian Engel, Christian Kuehn, Matteo Petrera +1
We study the problem of preservation of maximal canards for time discretized fast-slow systems with canard fold points. In order to ensure such preservation, certain favorable stru…
On fast-slow consensus networks with a dynamic weight
Hildeberto Jardón-Kojakhmetov, Christian Kuehn
We study dynamic networks under an undirected consensus communication protocol and with one state-dependent weighted edge. We assume that the aforementioned dynamic edge can take v…
Travelling Waves in Monostable and Bistable Stochastic Partial Differential Equations
Christian Kuehn
In this review, we provide a concise summary of several important mathematical results for stochastic travelling waves generated by monostable and bistable reaction-diffusion stoch…