二维积分-微分反应-扩散系统的时间周期振荡六方解

Pub Date : 2020-07-01 DOI:10.32917/hmj/1595901630

Shunsuke Kobayashi, T. Sakamoto, Yasuhide Uegata, S. Yazaki

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引用次数: 0

摘要

研究了一类具有非局域项的双组分反应扩散体系的振荡六方解。通过应用中心流形理论，我们得到了一个四维动力系统，它告诉我们围绕平凡解的分岔结构。我们的结果表明振荡六边形解可以通过Hopf分岔从静止六边形解分叉。这为振荡六边形的存在提供了一个合理的解释。

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A time-periodic oscillatory hexagonal solution in a 2-dimensional integro-differential reaction-diffusion system

An oscillatory hexagonal solution in a two component reaction-di¤usion 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.

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