171 citations · 411 across the 16 of their papers we have counts for
9 papers · 1 filter
(Un)predictability of strong El Niño events
John Guckenheimer, Axel Timmermann, Henk Dijkstra +1
The El Niño-Southern Oscillation (ENSO) is a mode of interannual variability in the coupled equatorial Pacific coupled atmosphere/ocean system. El Niño describes a state in which s…
Mixed mode oscillations of the El Niño-Southern Oscillation
Andrew Roberts, Esther Widiasih, Axel Timmermann +2
Very strong El Niño events occur sporadically every 10-20 years. The origin of this bursting behavior still remains elusive. Using a simplified 3-dimensional dynamical model of the…
Shilnikov Homoclinic Bifurcation of Mixed-Mode Oscillations
John Guckenheimer, Ian Lizarraga
The Koper model is a three-dimensional vector field that was developed to study complex electrochemical oscillations arising in a diffusion process. Koper and Gaspard described par…
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…