Codimension-Two Bifurcations in Animal Aggregation Models with Symmetry
Codimension-Two Bifurcations in Animal Aggregation Models with Symmetry
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DOI：
10.1137/130932272
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发表时间：
2014-11
期刊：
影响因子：
--
通讯作者：
P. Buono;R. Eftimie
中科院分区：
文献类型：
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作者：
P. Buono;R. Eftimie
自组织生物聚集中的模式形成是在过去20年中被深入研究的现象。一般来说，关于模式形成的研究主要集中在确定产生这些模式的生物学机制上。然而，确定这些模式背后的数学机制同样重要，因为它可以提供有关生物参数的信息，这些生物参数可能有助于某些模式的持续存在和其他模式的消失。此外，它还可以提供有关触发不同模式（与不同群体行为相关联）之间转换的机制的信息。在这篇文章中，我们专注于自组织聚集的一类非局部双曲模型，并证明这些模型是${\bfO（2）}}$-等变的。然后，我们使用群论方法，线性分析，弱非线性分析，和数值模拟来研究各种各样的模式，通过${\bf O（2）}}$-对称codeme.
Pattern formation in self-organized biological aggregation is a phenomenon that has been studied intensively over the past 20 years. In general, the studies on pattern formation focus mainly on identifying the biological mechanisms that generate these patterns. However, identifying the mathematical mechanisms behind these patterns is equally important, since it can offer information on the biological parameters that could contribute to the persistence of some patterns and the disappearance of other patterns. Also, it can offer information on the mechanisms that trigger transitions between different patterns (associated with different group behaviors). In this article, we focus on a class of nonlocal hyperbolic models for self-organized aggregations and show that these models are ${{\bf O(2)}}$-equivariant. We then use group-theoretic methods, linear analysis, weakly nonlinear analysis, and numerical simulations to investigate the large variety of patterns that arise through ${{\bf O(2)}}$-symmetric codime...