Self-organized anomalous aggregation of particles performing nonlinear and non-Markovian random walks
Self-organized anomalous aggregation of particles performing nonlinear and non-Markovian random walks
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DOI：
10.1103/physreve.92.062127
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发表时间：
2015-12-16
影响因子：
2.4
通讯作者：
Korabel, Nickolay
中科院分区：
文献类型：
--
作者：
Fedotov, Sergei;Korabel, Nickolay
我们提出了一种非线性和非马尔可夫随机游走模型，用于随机运动和能够感知人口密度的生物体的空间聚集。我们考虑了社会拥挤效应，其中分散率是人口密度和居住时间的递减函数。我们对随机游走进行随机模拟，发现自组织异常（SOA）现象，这会导致平稳聚合模式的崩溃。这种异常机制是自组织的，并且从一开始就不需要重尾等待时间分布。已经发现，当所有粒子聚集在一个微小域内（异常聚集）时，非线性随机游走会演变成异常状态。我们获得幂律平稳密度相关的生存函数，并将 SOA 的临界条件定义为平均停留时间的散度。讨论了初始条件在不同 SOA 场景中的作用。我们观察到短暂的异常双峰聚集现象。
We present a nonlinear and non-Markovian random walks model for stochastic movement and the spatial aggregation of living organisms that have the ability to sense population density. We take into account social crowding effects for which the dispersal rate is a decreasing function of the population density and residence time. We perform stochastic simulations of random walks and discover the phenomenon of self-organized anomaly (SOA), which leads to a collapse of stationary aggregation pattern. This anomalous regime is self-organized and arises without the need for a heavy tailed waiting time distribution from the inception. Conditions have been found under which the nonlinear random walk evolves into anomalous state when all particles aggregate inside a tiny domain (anomalous aggregation). We obtain power-law stationary density-dependent survival function and define the critical condition for SOA as the divergence of mean residence time. The role of the initial conditions in different SOA scenarios is discussed. We observe phenomenon of transient anomalous bimodal aggregation.