A Brief Review of Some Swarming Models Using Stochastic Differential Equations
A Brief Review of Some Swarming Models Using Stochastic Differential Equations
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一些使用随机微分方程的集群模型的简要回顾
DOI：
10.1007/978-981-16-5576-0_9
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Yagi Atsushi
中科院分区：
文献类型：
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作者：
Nguyen Linh Thi Hoai;Ta Ton Viet;Yagi Atsushi
本文简要回顾了我们在描述动物群体行为的随机微分方程模型方面所做的工作。我们首先提出了一个包含吸引、排斥和个体与环境相互作用的一般模型。环境可能包含障碍物或/和食物资源。此外，噪声因素，它反映了不完善的信息收集能力的个人和个人的行动的不完善的执行的个人的行为的不确定性的程度建模，也被考虑在内。其次，我们回顾了自由空间模型、避障模型和觅食模型，这些模型在一般模型中只需选择适当的外力即可得到。最后，我们展示了这些模型的一些数值模拟。数值模拟结果表明，群体行为与对真实的世界中动物行为的观察研究结果一致：动物在形成群体时具有觅食优势，在躲避障碍物时表现出不同的模式。更准确地说，我们观察到一组个体在避开球体障碍物时的四种行为模式，我们称之为反弹，拉回，通过和团聚，分离。具体来说，所有四种模式都可以通过调整一个参数而保持所有其他参数不变来实现。此外，我们发现模型参数，群体凝聚力，和行为模式之间的关系。
This paper gives a brief review of our work on stochastic differential equation (SDE) models describing the swarm behavior of animals. We firstly represent a general model which includes attraction, repulsion and individual–environment interaction. The environment may contain obstacles or/and food resource. In addition, a noise factor, which models the degree of uncertainty in the individual’s behavior that reflects both the imperfect information-gathering ability of an individual and the imperfect execution of the individual’s actions, is also taken into account. Secondly, we review free space model, avoiding obstacle model and foraging model, which can be obtained easily just by choosing an appropriate external force in the general model. Finally, we show some numerical simulations on these models. Our numerical study shows that the swarm behavior agrees well with the observation studies on animal’s behavior in the real world: animal enjoy foraging advantage while forming a swarm, they perform different patterns when avoiding obstacles. More precisely, we observe four behavioral patterns of a group of individuals while avoiding a sphere obstacle, which we call Rebound, Pullback, Pass and Reunion, Separation. Specifically, all four patterns can be achieved just by tuning one parameter while keeping all the others constant. Furthermore, we discover the relationship between model parameters, swarm cohesiveness, and behavioral patterns.