168 citations · 328 across the 19 of their papers we have counts for
14 papers · 1 filter
Stable and unstable spatially-periodic canards created in singular subcritical Turing bifurcations in the Brusselator system
Robert Jencks, Arjen Doelman, Tasso J. Kaper +1
In this article, we study the Brusselator partial differential equation (PDE) in the limit in which the diffusivity of the activator is much smaller than that of the inhibitor. The…
Multi-front dynamics in spatially inhomogeneous Allen-Cahn equations
Robbin Bastiaansen, Arjen Doelman, Tasso J. Kaper
Recent studies of biological, chemical, and physical pattern-forming systems have started to go beyond the classic `near onset' and `far from equilibrium' theories for homogeneous…
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…
Delayed bifurcation phenomena in reaction-diffusion equations: persistence of canards and slow passage through Hopf bifurcations
Tasso J. Kaper, Theodore Vo
In the context of a spatially extended model for the electrical activity in a pituitary lactotroph cell line, we establish that two delayed bifurcation phenomena from ODEs ---folde…