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Moving and jumping spot in a two dimensional reaction-diffusion model

Banff International Research Station for Mathematical Innovation and Discovery

We consider a single spot solution for the Schnakenburg Model in a two-dimensional unit disk in the singularly perturbed limit of a small diffusivity ratio. For large values of the reaction- time constant, this spot can undergo two different types of instabilities, both due to a Hopf bifurcation. The first type induces oscillatory instability in the height of the spot. The second type induces a periodic motion of the spot center. We use formal asymptotics to investigate when these instabilities are triggered, and which one dominates. In the parameter regime where spot motion occurs, we construct a periodic solution consisting of a rotating spot, and compute its radius of rotation and angular velocity.

Mathematics; Partial differential equations; Dynamical systems and ergodic theory

video/mp4

Author affiliation: Dalhousie

2017-01-30

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60086

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/