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Symmetry 2018, 10(4), 121; https://doi.org/10.3390/sym10040121

Stability of Bounded Dynamical Networks with Symmetry

ESIPP, University College Dublin, Dublin 4, Ireland
Received: 2 April 2018 / Revised: 12 April 2018 / Accepted: 13 April 2018 / Published: 19 April 2018
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Abstract

Motivated by dynamical models describing phase separation and the motion of interfaces separating phases, we study the stability of dynamical networks in planar domains formed by triple junctions. We take into account symmetry, angle-intersection conditions at the junctions and at the points at which the curves intersect with the boundary. Firstly, we focus on the case of a network where two triple junctions have all their branches unattached to the boundary and then on the case of a network of hexagons, with one of them having all its branches unattached to the boundary. For both type of networks, we introduce the evolution problem, identify the steady states and study their stability in terms of the geometry of the boundary. View Full-Text
Keywords: intersection; network; symmetry; nodes; geometry; differential; boundary intersection; network; symmetry; nodes; geometry; differential; boundary
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Dassios, I.K. Stability of Bounded Dynamical Networks with Symmetry. Symmetry 2018, 10, 121.

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