422 citations · 2.4k across the 156 of their papers we have counts for
6 papers · 2 filters
Normal Hyperbolicity and Unbounded Critical Manifolds
Christian Kuehn
This work is motivated by mathematical questions arising in differential equation models for autocatalytic reactions. In particular, this paper answers an open question posed by Gu…
Computing Slow Manifolds of Saddle Type
John Guckenheimer, Christian Kuehn
Slow manifolds are important geometric structures in the state spaces of dynamical systems with multiple time scales. This paper introduces an algorithm for computing trajectories…
Characterizing Slow Exit and Entrance Points
Christian Kuehn
Geometric Singular Perturbation Theory (GSPT) and Conley Index Theory are two powerful techniques to analyze dynamical systems. Conley already realized that using his index is easi…
From First Lyapunov Coefficients to Maximal Canards
Christian Kuehn
Hopf bifurcations in fast-slow systems of ordinary differential equations can be associated with surprising rapid growth of periodic orbits. This process is referred to as canard e…
Homoclinic Orbits of the FitzHugh-Nagumo Equation: Bifurcations in the Full System
John Guckenheimer, Christian Kuehn
This paper investigates travelling wave solutions of the FitzHugh-Nagumo equation from the viewpoint of fast-slow dynamical systems. These solutions are homoclinic orbits of a thre…
Homoclinic Orbits of the FitzHugh-Nagumo Equation: The Singular-Limit
John Guckenheimer, Christian Kuehn
The FitzHugh-Nagumo equation has been investigated with a wide array of different methods in the last three decades. Recently a version of the equations with an applied current was…