Spatially localized structures in the gray–Scott model

Punit Gandhi, Yuval R. Zelnik, Edgar Knobloch

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

Spatially localized structures in the one-dimensional Gray–Scott reaction–diffusion model are studied using a combination of numerical continuation techniques and weakly nonlinear theory, focusing on the regime in which the activator and substrate diffusivities are different but comparable. Localized states arise in three different ways: in a subcritical Turing instability present in this regime, and from folds in the branch of spatially periodic Turing states. They also arise from the fold of spatially uniform states. These three solution branches interconnect in complex ways. We use numerical continuation techniques to explore their global behaviour within a formulation of the model that has been used to describe dryland vegetation patterns on a flat terrain. This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)’.

Original languageEnglish
Article number20170375
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume376
Issue number2135
DOIs
StatePublished - 28 Dec 2018
Externally publishedYes

Keywords

  • Gray–Scott model
  • Localized structures
  • Turing instability

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering
  • General Physics and Astronomy

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