标题： 一种用于生物聚集的非局部连续体模型 显示英文标题

标题： A nonlocal continuum model for biological aggregation

摘要： 我们构建了一个连续体模型，用于描述生物聚集现象，其中个体经历长距离的社会吸引力和短距离的分散作用。 对于一维空间的情况，我们通过分析和数值方法研究了稳态。 存在具有紧支撑和陡峭边缘的强非线性状态，这些状态对应于局部生物聚集，或称为团块。 这些稳态团块通过动态粗化过程逐渐形成。 在大种群数量的极限情况下，团块趋于形成具有突变边缘的恒定密度群体。 我们使用能量论证来理解团块解的非线性选择，并预测大种群极限下的内部密度。 该能量结果同样适用于高维情况，并通过二维数值模拟进行了验证。 显示英文摘要

摘要： We construct a continuum model for biological aggregations in which individuals experience long-range social attraction and short range dispersal. For the case of one spatial dimension, we study the steady states analytically and numerically. There exist strongly nonlinear states with compact support and steep edges that correspond to localized biological aggregations, or clumps. These steady state clumps are approached through a dynamic coarsening process. In the limit of large population size, the clumps approach a constant density swarm with abrupt edges. We use energy arguments to understand the nonlinear selection of clump solutions, and to predict the internal density in the large population limit. The energy result holds in higher dimensions as well, and is demonstrated via numerical simulations in two dimensions.