149 citations · 164 across the 4 of their papers we have counts for
4 papers
From Canards of Folded Singularities to Torus Canards in a Forced van der Pol Equation
J. Burke, M. Desroches, A. Granados +3
We study canard solutions of the forced van der Pol (fvdP) equation in the relaxation limit for low-, intermediate-, and high-frequency periodic forcing. A central numerical observ…
Localised states in an extended Swift-Hohenberg equation
John Burke, Jonathan H. P. Dawes
Recent work on the behaviour of localised states in pattern forming partial differential equations has focused on the traditional model Swift-Hohenberg equation which, as a result…
A showcase of torus canards in neuronal bursters
John Burke, Mathieu Desroches, Anna M. Barry +2
Rapid action potential generation --- spiking --- and alternating intervals of spiking and quiescence --- bursting --- are two dynamic patterns observed in neuronal activity. In co…
Snakes and ladders: localized solutions of plane Couette flow
Tobias M. Schneider, John F. Gibson, John Burke
We demonstrate the existence of a large number of exact solutions of plane Couette flow, which share the topology of known periodic solutions but are localized in space. Solutions…