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Pattern formation in nonlocal Kondo model
Author(s) -
Cygan Szymon
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7448
Subject(s) - mathematics , bifurcation , fixed point theorem , guppy , bifurcation theory , fixed point , reaction–diffusion system , mathematical analysis , point (geometry) , statistical physics , fish <actinopterygii> , geometry , nonlinear system , physics , quantum mechanics , fishery , biology
We study a nonlocal evolution equation generalising a model introduced by Shigeru Kondo to explain colour patterns on a skin of a guppy fish. We prove the existence of stationary solutions using either the bifurcation theory or the Schauder fixed‐point theorem. We also present numerical studies of this model and show that it exhibits patterns similar to those modelled by well‐known reaction‐diffusion equations.