Coagulation–Fragmentation Model for Animal Group-Size Statistics
Coagulation–Fragmentation Model for Animal Group-Size Statistics
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DOI：
10.1007/s00332-016-9336-3
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发表时间：
2015-10
影响因子：
3
通讯作者：
P. Degond;Maximilian Engel
中科院分区：
文献类型：
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作者：
P. Degond;Maximilian Engel
我们研究受渔业科学中提出的一个简单模型启发的凝固破碎方程，以解释远洋鱼类鱼群大小分布的数据。尽管这些方程缺乏详细的平衡并且承认noh定理，但基于Bernstein和Pick函数的复函数理论的最新发展，我们能够对平衡剖面和大时间行为进行相当完整的描述。在大种群连续体极限下，达到了一个标度不变状态，其中所有的平衡都由一个标度曲线决定。这个通用的剖面表现出幂律行为，从小尺寸的指数到大尺寸的指数，具有指数截止。
We study coagulation–fragmentation equations inspired by a simple model proposed in fisheries science to explain data for the size distribution of schools of pelagic fish. Although the equations lack detailed balance and admit noH-theorem, we are able to develop a rather complete description of equilibrium profiles and large-time behavior, based on recent developments in complex function theory for Bernstein and Pick functions. In the large-population continuum limit, a scaling-invariant regime is reached in which all equilibria are determined by a single scaling profile. This universal profile exhibits power-law behavior crossing over from exponentfor small size tofor large size, with an exponential cutoff.