41 citations · 239 across the 19 of their papers we have counts for
3 papers · 2 filters
The dynamics of localized spot patterns for reaction-diffusion systems on the sphere
Philippe H. Trinh, Michael J. Ward
In the singularly perturbed limit corresponding to a large diffusivity ratio between two components in a reaction-diffusion (RD) system, quasi-equilibrium spot patterns are often a…
Stripe to spot transition in a plant root hair initiation model
V. F. Breña-Medina, D. Avitabile, A. R. Champneys +1
A generalised Schnakenberg reaction-diffusion system with source and loss terms and a spatially dependent coefficient of the nonlinear term is studied both numerically and analytic…
Slowly varying control parameters, delayed bifurcations and the stability of spikes in reaction-diffusion systems
Justin C. Tzou, Michael J. Ward, Theodore Kolokolnikov
We present three examples of delayed bifurcations for spike solutions of reaction-diffusion systems. The delay effect results as the system passes slowly from a stable to an unstab…