Unilateral regulation breaks regularity of Turing patterns

Tomáš Vejchodský, Filip Jaroš, Milan Kučera, and Vojtěch Rybář
Phys. Rev. E 96, 022212 – Published 22 August 2017

Abstract

We consider a reaction-diffusion system undergoing Turing instability and augment it by an additional unilateral source term. We investigate its influence on the Turing instability and on the character of resulting patterns. The nonsmooth positively homogeneous unilateral term τv has favorable properties, but the standard linear stability analysis cannot be performed. We illustrate the importance of the nonsmoothness by a numerical case study, which shows that the Turing instability can considerably change if we replace this term by its arbitrarily precise smooth approximation. However, the nonsmooth unilateral term and all its approximations yield qualitatively similar patterns although not necessarily developing from small disturbances of the spatially homogeneous steady state. Further, we show that the unilateral source breaks the approximate symmetry and regularity of the classical patterns and yields asymmetric and irregular patterns. Moreover, a given system with a unilateral source produces spatial patterns even for diffusion parameters with ratios closer to 1 than the same system without any unilateral term.

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  • Received 19 April 2017

DOI:https://doi.org/10.1103/PhysRevE.96.022212

©2017 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Nonlinear Dynamics

Authors & Affiliations

Tomáš Vejchodský1,*, Filip Jaroš2,†, Milan Kučera1,3,‡, and Vojtěch Rybář1,§

  • 1Institute of Mathematics, Czech Academy of Sciences, Žitná 25, CZ-115 67 Praha 1, Czech Republic
  • 2Faculty of Arts, University of Hradec Králové, náměstí Svobody 331, CZ-500 02 Hradec Králové, Czech Republic
  • 3Department of Mathematics, Faculty of Applied Sciences, University of West Bohemia in Pilsen, Univerzitní 8, 30614 Plzeň, Czech Republic

  • *vejchod@math.cas.cz
  • filip.jaros@uhk.cz
  • kucera@math.cas.cz
  • §rybar@math.cas.cz

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Issue

Vol. 96, Iss. 2 — August 2017

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