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Unilateral regulation breaks regularity of Turing patterns

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    0477232 - MÚ 2018 RIV US eng J - Journal Article
    Vejchodský, Tomáš - Jaroš, F. - Kučera, Milan - Rybář, Vojtěch
    Unilateral regulation breaks regularity of Turing patterns.
    Physical Review E. Roč. 96, č. 2 (2017), č. článku 022212. ISSN 2470-0045
    EU Projects: European Commission(XE) 328008 - STOCHDETBIOMODEL
    Institutional support: RVO:67985840
    Keywords : unilateral term * Turing instability * pattern
    Subject RIV: BA - General Mathematics
    OBOR OECD: Applied mathematics
    Impact factor: 2.284, year: 2017

    We consider a reaction-diffusion system undergoing Turing instability and augment it by an additional unilateral nonsmooth unilateral source term. We investigate its influence on the Turing instability and on the character of resulting patterns. 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. 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 systém with a unilateral source produces spatial patterns even for diffusion parameters with ratios closer to 1 than the same systém without any unilateral term.
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