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July 2020 A time-periodic oscillatory hexagonal solution in a 2-dimensional integro-differential reaction-diffusion system
Shunsuke Kobayashi, Takashi Okuda Sakamoto, Yasuhide Uegata, Shigetoshi Yazaki
Hiroshima Math. J. 50(2): 253-267 (July 2020). DOI: 10.32917/hmj/1595901630

Abstract

An oscillatory hexagonal solution in a two component reaction-diffusion system with a non-local term is studied. By applying the center manifold theory, we obtain a four-dimensional dynamical system that informs us about the bifurcation structure around the trivial solution. Our results suggest that the oscillatory hexagonal solution can bifurcate from a stationary hexagonal solution via the Hopf bifurcation. This provides a reasonable explanation for the existence of the oscillatory hexagon.

Citation

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Shunsuke Kobayashi. Takashi Okuda Sakamoto. Yasuhide Uegata. Shigetoshi Yazaki. "A time-periodic oscillatory hexagonal solution in a 2-dimensional integro-differential reaction-diffusion system." Hiroshima Math. J. 50 (2) 253 - 267, July 2020. https://doi.org/10.32917/hmj/1595901630

Information

Received: 14 September 2019; Revised: 3 February 2020; Published: July 2020
First available in Project Euclid: 28 July 2020

zbMATH: 07256507
MathSciNet: MR4132591
Digital Object Identifier: 10.32917/hmj/1595901630

Subjects:
Primary: 35K57, 37G15
Secondary: 37G05, 37M05

Rights: Copyright © 2020 Hiroshima University, Mathematics Program

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Vol.50 • No. 2 • July 2020
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