Lutscher Frithjof
Biomathematik, Auf der Morgenstelle 10, Universität Tübingen, Germany.
J Math Biol. 2002 Sep;45(3):234-60. doi: 10.1007/s002850200146.
Schools of fish and flocks of birds are examples for groups of individuals moving in a highly organized way. Individuals adapt their orientation and speed to that of their (nearest) neighbors. Adaptation of orientation can also be found on the cellular and subcellular level and is called alignment. A model for alignment and movement is derived on the basis of reaction transport equations in one space dimension. Existence of solutions is shown and long time behavior of the system is described. The effect of schooling on the risk of predation is investigated. Then the model is generalized to two space dimensions and compared to other models for alignment which do not incorporate individual movement in space.
鱼群和鸟群是个体以高度有组织的方式移动的群体的例子。个体根据其（最近的）邻居的方向和速度来调整自己的方向和速度。方向的适应性在细胞和亚细胞水平上也能发现，这被称为排列。基于一维空间中的反应输运方程推导了一个排列和运动的模型。证明了解的存在性并描述了系统的长期行为。研究了群体行为对被捕食风险的影响。然后将该模型推广到二维空间，并与其他不考虑个体在空间中运动的排列模型进行比较。
