171 citations · 411 across the 16 of their papers we have counts for
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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…
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…
Rigorous Enclosures of a Slow Manifold
John Guckenheimer, Tomas Johnson, Philipp Meerkamp
Slow-fast dynamical systems have two time scales and an explicit parameter representing the ratio of these time scales. Locally invariant slow manifolds along which motion occurs o…