Research Page
The Stability of Stripes and Mesas for Reaction-Diffusion Systems
description to be written; pictures and movies
- The Stability of a
Stripe for the Gierer-Meinhardt Model and the Effect of Saturation
with T. Kolokolnikov, W. Sun, and J. Wei (SIAM J. Appl.
Dyn. Systems, Vol. 5, No. 2, (2006), pp. 313-363.)
-
Zigzag and Breakup Instabilities of Stripes and Rings in the
Two-Dimensional Gray-Scott Model
with T. Kolokolnikov and J. Wei
(Studies in Appl. Math., Vol. 16, No. 1, (2006), pp. 35-95.)
-
Self-Replication of Mesa Patterns in Reaction-Diffusion Systems
with T. Kolokolnikov and J. Wei (Physica D, Vol. 236, No. 2,
(2007), pp. 104-122).
- Stripe to Spot Transition
in a Plant Root Hair Initiation Model
Victor Brena-Medina, D. Avitabile, A. Champneys, M.J. Ward,
(SIAM J. Appl. Math, Vol. 75, No. 3, (2015), pp. 1090-1119.)
- Explicitly Solvable Nonlocal
Eigenvalue Problems and the Stability of Localized Stripes in
Reaction-Diffusion Systems
with I. Moyles, W. H. Tse, (Studies in Applied Math, Vol. 136, No. 1,
(2016), pp. 89-136.)
- Existence, Stability, and Dynamics
of Ring and Near-Ring Solutions to the Gierer-Meinhardt Model with
Saturation in the Semi-Strong Regime
with Iain Moyles (SIAM J. Appl. Dyn. Systems, Vol. 16, No. 1, (2017),
pp. 597-639).
- Stabilizing a Homoclinic
Stripe
with Theodore Kolokolnikov, Justin Tzou, and Juncheng Wei (
Philos. Trans. A Math Phys Eng. Sci. 2018 Nov 12;376(20135).}