University of Sussex
Browse
Manuscript-ColourV[1].pdf (2.65 MB)

Turing pattern formation under heterogeneous distributions of parameters for an activator-depleted reaction model

Download (2.65 MB)
journal contribution
posted on 2023-06-09, 23:18 authored by David Hernandez-Aristizabal, Diego A Garzon-Alvarado, Anotida MadzvamuseAnotida Madzvamuse
The purpose of this article is to study Turing pattern formation in one- and two-dimensional domains under heterogeneous distributions of the parameters for an activator-depleted model. Unlike previous studies of this nature, the choice of the heterogeneous distributions of the parameters is closely linked and estimated by use of rigorous wave mode selection in order to excite different modes in different subsets of the domains. This allows us to relate the numerical solutions with theoretical linear stability analytical results. Our most revealing results show that the wave modes of adjacent subsets evolve locally and yet possess continuity across the interface. These local patches of the solutions result in a globally heterogeneous solution stable only in the presence of heterogeneous distributions of the parameters. Furthermore, our results show that initial conditions continue to play a crucial role in the selection of excitable wave modes and consequently the formation of the inhomogeneous patterns formed. In particular, initial conditions influence pattern orientation and polarity, and yet with a prepattern, the patterns conserved orientation and polarity. Numerical solutions are obtained by the use of the finite element method and the backward Euler scheme to deal with the spatial and the time discretisations, respectively.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Journal of Nonlinear Science

ISSN

0938-8974

Publisher

Springer

Issue

a34

Volume

31

Page range

1-27

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2021-03-12

First Open Access (FOA) Date

2022-03-10

First Compliant Deposit (FCD) Date

2021-03-11

Usage metrics

    University of Sussex (Publications)

    Categories

    No categories selected

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC