Influence of Boundaries on Localized Patterns | Zendy

Gregory Kozyreff | Zendy; Pauline Assémat | Zendy; S. Jonathan Chapman | Zendy

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Influence of Boundaries on Localized Patterns

Author(s) -

Gregory Kozyreff,

Pauline Assémat,

S. Jonathan Chapman

Publication year - 2009

Publication title -

physical review letters

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.688

H-Index - 673

eISSN - 1079-7114

pISSN - 0031-9007

DOI - 10.1103/physrevlett.103.164501

Subject(s) - homoclinic orbit , instability , bifurcation , bifurcation diagram , physics , domain (mathematical analysis) , boundary (topology) , statistical physics , pattern formation , range (aeronautics) , homoclinic bifurcation , boundary value problem , turing , phase diagram , diagram , classical mechanics , mathematical analysis , condensed matter physics , mechanics , mathematics , quantum mechanics , materials science , computer science , nonlinear system , phase (matter) , statistics , composite material , biology , genetics , programming language

We analytically study the influence of boundaries on distant localized patterns generated by a Turing instability. To this end, we use the Swift-Hohenberg model with arbitrary boundary conditions. We find that the bifurcation diagram of these localized structures generally involves four homoclinic snaking branches, rather than two for infinite or periodic domains. Second, steady localized patterns only exist at discrete locations, and only at the center of the domain if their size exceeds a critical value. Third, reducing the domain size increases the pinning range

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