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Influence of Boundaries on Localized Patterns

Abstract : 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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Gregory Kozyreff, Pauline Assemat, Stephen Jonathan Chapman. Influence of Boundaries on Localized Patterns. Physical Review Letters, American Physical Society, 2009, vol. 103 (n° 16), pp. 164501/1-164501/4. ⟨10.1103/PhysRevLett.103.164501⟩. ⟨hal-01785105⟩

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