一个产生不对称涡旋的自驱动粒子模型

生物群体运动形成涡旋是自然界中经常出现的现象, 很多学者对其机制进行研究, 机制模型可使群体达到对称的涡旋形态. 然而自然界中大多数生物群体形成的涡旋并不是对称的. 本文引入个体空间感知各向异性的因素, 对产生群体对称涡旋的自驱动粒子模型进行研究. 我们提出模型的基本假设是: 个体对纵向距离的感知短于真实纵向距离, 而横向距离的认知没有偏差. 这造成个体之间相互作用强度各向异性. 模拟结果表明: 当这种偏差达到一定程度时, 群体最终呈现并维持在更符合实际情况的偏心涡旋状态. 这表明空间感知的各向异性可能正是造成实际生物系统中群体形成偏心涡旋而非对称涡旋的原因. 本文还对模型进行了参数敏感性分析, 结果表明: 当群体的对齐倾向比较弱时, 较小的距离知觉偏差对群体的行为没有影响, 适中的偏差会使群体出现偏心涡旋, 过大的偏差会使群体陷入混乱; 当群体的对齐倾向较强时, 较小的距离知觉偏差不会改变群体对齐的现象, 而较大的偏差会使群体出现偏心涡旋, 过大的偏差会使群体陷入混乱. 

A self-propelling particle model displaying an asymmetric vortex

Vortex formation in biological grouping is very common in nature.Works have been done formation mechanism,some models could achieve a symmetrical vortex shape.But in most cases the vortex formed by living organisms is not symmetrical.In the present work,self-driven particle model producing a symmetric vortex was studied,introducing the factor of individual spatial perceptual anisotropy.The basic hypothesis is that perception of longitudinal distance is shorter than the true longitudinal distance while lateral distance is not biased.But this would result in anisotropy of the strength of agent interactions.Simulations revealed that when deviation reached a certain level,the population finally resents and maintains an eccentric vortex state,which coincided with the actual situation better.This would indicate that for a living group to form an asymmetric rather than a symmetric vortex,spatial perceptual anisotropy may be the major reason Parameter sensitivity analysis revealed that when group aligning tendency was weak,small distance perception deviation had no effect on group behavior;moderate deviation made the group appear as eccentric vortex,excessive deviation would make the group into a mess.With strong aligning tendency,moderate distance perception deviation could not change the ending with alignment,but large deviation would make the group appear as eccentric vortex;excessive deviation resulted in group disorder.