Weakly nonlinear analysis of a hyperbolic model for animal group formation
Weakly nonlinear analysis of a hyperbolic model for animal group formation
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DOI：
10.1007/s00285-008-0209-8
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发表时间：
2009-07-01
影响因子：
1.9
通讯作者：
Lewis, M. A.
中科院分区：
文献类型：
--
作者：
Eftimie, R.;de Vries, G.;Lewis, M. A.
我们考虑一个一维的非局部双曲模型与应用程序的自组织集体的动物在均匀环境中的群体形成。以往的研究表明，该模型显示至少四个复杂的空间和时空组模式。在这里，我们使用弱非线性分析，以更好地了解这些模式，即平稳脉冲和列车的形成机制。我们发现，这两种模式产生的亚临界分岔空间均匀的稳定状态。然后，我们使用这些结果来研究两种社会相互作用（吸引力和对齐）对固定和移动动物群体结构的影响。虽然吸引力使群体更加紧密，但对齐具有双重效果，这取决于群体是静止的还是移动的。更确切地说，增加对齐使固定组紧凑，并且使移动组更细长。此外，研究结果表明，存在一个阈值的总群体密度，在此之上，静态和移动群体描述的协调行为持续很长一段时间。
We consider an one-dimensional nonlocal hyperbolic model for group formation with application to self-organizing collectives of animals in homogeneous environments. Previous studies have shown that this model displays at least four complex spatial and spatiotemporal group patterns. Here, we use weakly nonlinear analysis to better understand the mechanisms involved in the formation of two of these patterns, namely stationary pulses and traveling trains. We show that both patterns arise through subcritical bifurcations from spatially homogeneous steady states. We then use these results to investigate the effect of two social interactions (attraction and alignment) on the structure of stationary and moving animal groups. While attraction makes the groups more compact, alignment has a dual effect, depending on whether the groups are stationary or moving. More precisely, increasing alignment makes the stationary groups compact, and the moving groups more elongated. Also, the results show the existence of a threshold for the total group density, above which, coordinated behaviors described by stationary and moving groups persist for a long time.