Biological Aggregation Driven by Social and Environmental Factors: A Nonlocal Model and Its Degenerate Cahn Hilliard Approximation
Biological Aggregation Driven by Social and Environmental Factors: A Nonlocal Model and Its Degenerate Cahn Hilliard Approximation
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DOI：
10.1137/15m1031151
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发表时间：
2016-01-01
影响因子：
2.1
通讯作者：
Topaz, Chad M.
中科院分区：
文献类型：
--
作者：
Bernoff, Andrew J.;Topaz, Chad M.
昆虫群和鸟群等生物聚集可能是社会互动和环境因素共同作用的结果。我们专注于非局部连续方程，这是经常被用来模拟聚集，但这带来了重大的分析和计算挑战。从一个特定的非局部聚集模型开始[C。M.黄玉，A. L. Bertozzi和M. A.刘易斯，布尔。数学。生物。68（2006），pp. 1601-1623]，我们得到了最小适定长波近似，它是一个退化的Cahn-Hilliard方程.能量最小化，这种减少，本地模型保留了许多显着的特点，那些非本地模型，特别是对于大人口和远离聚集的边界。使用Cahn-Hilliard模型作为试验平台，我们调查了外部潜在建模食物来源可以用来抑制峰值人口密度的程度，这对于控制蝗虫暴发至关重要。食物来源的随机分布倾向于增加峰值密度超过其固有值，而食物来源的周期性模式可以降低峰值密度。
Biological aggregations such as insect swarms and bird flocks may arise from a combination of social interactions and environmental cues. We focus on nonlocal continuum equations, which are often used to model aggregations, and yet which pose significant analytical and computational challenges. Beginning with a particular nonlocal aggregation model [C. M. Topaz, A. L. Bertozzi, and M. A. Lewis, Bull. Math. Bio., 68 (2006), pp. 1601-1623], we derive the minimal well-posed long wave approximation, which is a degenerate Cahn-Hilliard equation. Energy minimizers of this reduced, local model retain many salient features of those of the nonlocal model, especially for large populations and away from an aggregation's boundaries. Using the Cahn-Hilliard model as a testbed, we investigate the degree to which an external potential modeling food sources can be used to suppress peak population density, which is essential for controlling locust outbreaks. A random distribution of food sources tends to increase peak density above its intrinsic value, while a periodic pattern of food sources can decrease it.