Pattern formation in nonlocal Kondo model. (16th May 2021)

• Record Type: Journal Article
• Authors: Cygan, Szymon
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 13(2021)
• Page Start: 10804
• Page End: 10822
• Publication Date: 2021-05-16
• Subjects: convolution operators -- Kondo model -- numerical simulations -- patterns formation -- Rabinowitz bifurcation theorem -- Schauder fixed‐point theorem; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7448
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : 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.