羊群体运动元胞自动机模型中的最小势能分析

Analysis of the minimum potential energy in the cellular automaton model of sheep flock movement

[目的]群体运动作为大自然最普遍的现象,依据不同社会条件,个体会有不同的集体运动展现。其中,从众现象中的旋转是最普遍的群体运动,尽管研究人员对羊群运动进行过一些研究,但羊群旋转行为的机理尚不清楚。为了探讨动物群体运动与势能之间的关系,本文对自然界中300 m×300 m牧场中的100只羊进行观察。[方法]假设羊群运动受到势能控制,以前的研究大多提出复杂的模型,且对群体多种运动状态分析不足,本文基于最小势能原理结合元胞自动机模拟羊群体运动。通过定义避障、随机、随波逐流、加速运动等基本行为,用多个元胞空间分割牧场,同时以“羊”为元胞中心划分9个元胞空间代表周围环境,通过与参考邻居“p”的距离势能进行比较确定下一步移动轨迹。[结果]空间范围内羊群体运动会形成多种形式,但当运动系统遵从耗能最小运动时,群体形态有可能以旋转漩涡形式展示。建立的最小势能元胞自动机模型能够较好的描述羊群体运动各种行为机理,最小能量原理作为生态系统基本定律,模拟说明羊的群体运动是符合最小势能原理的,进一步说明动物间群体动物间群体运动同样依照此原理形成转圈、并排、三角阵形等行为。[结论]本研究打开了畜牧业群体运动的研究新方向,为羊群的管理提供理论指并奠定实践基础。

[Objective]Group movement is the most common phenomenon in nature, and individuals have different collective movement displays according to different social conditions. Among them,the rotation in the herd mentality is the most prevalent group movement. Although researchers have conducted some studies on sheep flock movement, the mechanism of sheep flock rotation behavior is not clear. In order to explore the relationship between animal group movement and potential energy, 100 sheep in a 300 m×300 m pasture in the field were observed.[Methods]Assuming that sheep movement is controlled by potential energy, previous researchers have mostly proposed complex models and have inadequate analysis of multiple movement states of the group. Therefore, this paper used the principle of minimum potential energy in combination with cellular automaton simulation to study the movement of sheep herds. Basic behaviors such as obstacle avoidance, random movement, following the flow,and accelerated movement were defined,and the pasture was divided into multiple cellular spaces. Nine cellular spaces were used to represent the surrounding environment with the "sheep" at the center. The next movement trajectory was determined by comparing the distance potential energy with reference neighbor "p".[Results]Sheep group movement within a spatial range took on many forms, but when the movement system conformed to the minimum energy movement, the group form may take on the form of a rotating vortex. The established minimal potential energy cellular automaton model can better describe the various behavioral mechanisms of sheep group movement. The principle of minimal energy, as a basic law of the ecosystem,simulated that sheep’s herd movement was in accordance with the minimal potential energy principle,further indicating that the movement of animal groups also followed this principle, forming behaviors such as circling, parallel, and triangular formation. [Conclusion]This study opens up a new direction for the research of group movement in animal husbandry and provides a theoretical guidelines and practical basis for the sheep management.