Simple pde model of spot replication in any dimension
Journal
SIAM Journal on Mathematical Analysis
Journal Volume
44
Journal Issue
5
Pages
3564-3593
Date Issued
2012
Author(s)
Kolokolnikov, T.
Abstract
We propose a simple PDE model which exhibits self-replication of spot solutions in any dimension. This model is analyzed in one and higher dimensions. In the radially symmetric case, we rigorously demonstrate that a weakened version of the conditions proposed by Nishiura and Ueyama for self-replication are satisfied. In dimension three, two different types of replication mechanisms are analyzed. The first type is due to radially symmetric instability, whereby a spot bifurcates into a ring. The second type is nonradial instability, which causes a spot to deform into a peanut-like shape and eventually split into two spots. Both types of replication are observed in our model, depending on parameter choice. Numerical simulations are shown confirming our analytical results.
SDGs
Type
journal article