From one pattern into another: analysis of Turing patterns in heterogeneous domains via WKBJ.

ABSTRACT: Pattern formation from homogeneity is well studied, but less is known concerning symmetry-breaking instabilities in heterogeneous media. It is non-trivial to separate observed spatial patterning due to inherent spatial heterogeneity from emergent patterning due to nonlinear instability. We employ WKBJ asymptotics to investigate Turing instabilities for a spatially heterogeneous reaction-diffusion system, and derive conditions for instability which are local versions of the classical Turing conditions. We find that the structure of unstable modes differs substantially from the typical trigonometric functions seen in the spatially homogeneous setting. Modes of different growth rates are localized to different spatial regions. This localization helps explain common amplitude modulations obser

SUBMITTER: Krause AL 

PROVIDER: S-EPMC7014807 | biostudies-literature | 2020 Jan

REPOSITORIES: biostudies-literature