27 citations · 98 across the 12 of their papers we have counts for
5 papers · 1 filter
Pitchfork bifurcation along a slow parameter ramp: coherent structures in the critical scaling
Ryan Goh, Tasso J. Kaper, Arnd Scheel
We investigate the slow passage through a pitchfork bifurcation in a spatially extended system, when the onset of instability is slowly varying in space. We focus here on the criti…
Fronts in the wake of a parameter ramp: slow passage through pitchfork and fold bifurcations
Ryan Goh, Tasso J. Kaper, Arnd Scheel +1
This work studies front formation in the Allen-Cahn equation with a parameter heterogeneity which slowly varies in space. In particular, we consider a heterogeneity which mediates…
Delayed Hopf bifurcation and space-time buffer curves in the Complex Ginzburg-Landau equation
Ryan Goh, Tasso J. Kaper, Theodore Vo
In this article, the phenomenon of delayed Hopf bifurcations (DHB) in reaction-diffusion PDEs is analyzed in the cubic Complex Ginzburg-Landau equation with a slowly-varying parame…
Pattern formation in the wake of triggered pushed fronts
Ryan Goh, Arnd Scheel
Pattern-forming fronts are often controlled by an external stimulus which progresses through a stable medium at a fixed speed, rendering it unstable in its wake. By controlling the…
Triggered Fronts in the Complex Ginzburg Landau Equation
Ryan Goh, Arnd Scheel
We study patterns that arise in the wake of an externally triggered, spatially propagating instability in the complex Ginzburg-Landau equation. We model the trigger by a spatial in…