142 citations · 214 across the 6 of their papers we have counts for
6 papers
First passage times in integrate-and-fire neurons with stochastic thresholds
Wilhelm Braun, Paul C. Matthews, Rüdiger Thul
We consider a leaky integrate-and-fire neuron with deterministic subthreshold dynamics and a firing threshold that evolves as an Ornstein-Uhlenbeck process. The formulation of this…
Variational approximations to homoclinic snaking in continuous and discrete systems
P. C. Matthews, H. Susanto
Localised structures appear in a wide variety of systems, arising from a pinning mechanism due to the presence of a small-scale pattern or an imposed grid. When there is a separati…
The Nikolaevskiy equation with dispersion
Eman Simbawa, Paul C. Matthews, Stephen M. Cox
The Nikolaevskiy equation was originally proposed as a model for seismic waves and is also a model for a wide variety of systems incorporating a neutral, Goldstone mode, including…
Pattern formation in the damped Nikolaevskiy equation
S. M. Cox, P. C. Matthews
The Nikolaevskiy equation has been proposed as a model for seismic waves, electroconvection and weak turbulence; we show that it can also be used to model transverse instabilities…
Bifurcation in two-dimensional fixed point subspaces
P. C. Matthews
Bifurcation with symmetry is considered in the case of an isotropy subgroup with a two-dimensional fixed point subspace and non-zero quadratic terms. In general, there are one or t…
Pattern formation with a conservation law
P. C. Matthews, S. M. Cox
Pattern formation in systems with a conserved quantity is considered by studying the appropriate amplitude equations. The conservation law leads to a large-scale neutral mode that…