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).}