Pattern formation in reaction-diffusion models with nonuniform domain growth
Pattern formation in reaction-diffusion models with nonuniform domain growth
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DOI：
10.1006/bulm.2002.0295
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发表时间：
2002-07-01
影响因子：
3.5
通讯作者：
Maini, PK
中科院分区：
文献类型：
--
作者：
Crampin, EJ;Hackborn, WW;Maini, PK
最近的生物模式形成的例子，其中模式随着基础领域的增长而发生质的变化，引起了人们对模式形成的反应扩散（图灵）模型的新兴趣。几位作者现在报告的研究表明，通过增加域增长，图灵模型可以生成与实验观察结果一致的模式序列。这些研究证明了浓度峰响应域生长而对称分裂或插入的趋势。该过程也被建议作为可靠模式选择的机制。然而，到目前为止，作者只考虑了整个域中生长均匀的有限情况。在本文中，我们概括了最近在生长域上形成反应扩散模式的结果，以考虑空间不均匀生长的影响。目的是双重的：首先证明添加弱空间异质性不会显着改变均匀情况下的模式选择，但其次，足够强的不均匀性（例如，只有域的有限部分在生长）可以产生均匀情况下未见的模式序列，从而提供控制模式选择的进一步机制。提出了一个建模框架，其中域扩展和边界（顶端）增长以一致的方式统一。结果对所有受潜在域增长影响的反应扩散类型模型都有影响。 (C) 2002 年数学生物学学会。由爱思唯尔科学有限公司出版。保留所有权利。
Recent examples of biological pattern formation where a pattern changes qualitatively as the underlying domain grows have given rise to renewed interest in the reaction-diffusion (Turing) model for pattern formation. Several authors have now reported studies showing that with the addition of domain growth the Turing model can generate sequences of patterns consistent with experimental observations. These studies demonstrate the tendency for the symmetrical splitting or insertion of concentration peaks in response to domain growth. This process has also been suggested as a mechanism for reliable pattern selection. However, thus far authors have only considered the restricted case where growth is uniform throughout the domain.In this paper we generalize our recent results for reaction-diffusion pattern formation on growing domains to consider the effects of spatially nonuniform growth. The purpose is twofold: firstly to demonstrate that the addition of weak spatial heterogeneity does not significantly alter pattern selection from the uniform case, but secondly that sufficiently strong nonuniformity, for example where only a restricted part of the domain is growing, can give rise to sequences of patterns not seen for the uniform case, giving a further mechanism for controlling pattern selection. A framework for modelling is presented in which domain expansion and boundary (apical) growth are unified in a consistent manner. The results have implications for all reaction-diffusion type models subject to underlying domain growth. (C) 2002 Society for Mathematical Biology. Published by Elsevier Science Ltd. All rights reserved.