非线性相互作用诱导的鸽群运动方向的有序切换  

Nonlinear interaction-induced ordered directional switches in pigeon flocks

作　　者：肖瑞 李望 刘世杰 陈都鑫 孙永征 Rui XIAO;Wang LI;Shijie LIU;Duxin CHEN;Yongzheng SUN(School of Mathematics,China University of Mining and Technology,Xuzhou 221116,China;Jiangsu Center for Applied Mathematics(CUMT),Xuzhou 221116,China;School of Mathematics,Southeast University,Nanjing 211096,China)

机构地区：[1]中国矿业大学数学学院,徐州221116 [2]江苏省应用数学(中国矿业大学)中心,徐州221116 [3]东南大学数学学院,南京211096

出　　处：《中国科学:信息科学》2025年第2期412-425,共14页Scientia Sinica(Informationis)

基　　金：国家自然科学基金(批准号:12302040,12271519);江苏省自然科学基金(批准号:BK20221107);徐州市自然科学基金(批准号:KC23065);中央高校基本科研业务费专项资金(批准号:2024KYJD2003)资助项目。

摘　　要：在许多动物群体的运动中,其在方向上突然连贯的变化是一重要且普遍存在的现象.对鸽群和蝗虫群的观察表明,方向切换是它们运动的内在特性.已有研究表明,自驱动粒子模型可以用来描述群体运动的方向切换行为.理解决定方向切换行为的因素是理解群体运动的关键.本文重点研究社交和非线性相互作用对鸽群方向切换行为的影响.基于降维理论框架,将高维复杂模型简化为一维简单模型,对一维模型理论分析得到稳态概率密度和平均切换时间.对于稳态概率密度,一维模型得到的理论结果和高维模型得到的数值结果一致,说明降维和理论分析方法的有效性.研究结果表明社交和非线性相互作用在调节鸽群的方向切换行为中起着重要作用.具体来说,群密度和网络平均度的增加可以抑制方向切换行为.然而,非线性参数对方向切换行为的影响是非单调的,当非线性参数较小时,其增加首先抑制方向切换行为,而继续增加可以促进方向切换行为.非线性参数的增加使群体的运动从有序逐渐转变为无序切换.研究结果揭示了社交和非线性相互作用在鸽群运动方向切换中的作用机制,为设计无人机集群的控制策略提供理论依据.In the movement of many animal groups,their sudden and coherent changes in direction constitute a significant and ubiquitous phenomenon.Observations of pigeons and locusts have shown that such directional switching behavior is an intrinsic property of their motion.Previous studies have demonstrated that the self-driven particle model can be utilized to elucidate the directional switching behavior observed in group motion.Comprehending the factors that influence these switches is pivotal to understanding the underlying mechanisms of collective movement.In this paper,we delve into the infuence of social and nonlinear interactions on the directional switching behavior within pigeon focks.Based on the dimension reduction approach,the high-dimensional complex model has been collapsed into the one-dimensional model,then we can derive the theoretical estimation of stationary probability density and mean switching time(MST).The theoretical results for the stationary probability density derived from the one-dimensional model are consistent with the numerical ones obtained from the high-dimensional model,indicating the effectiveness of the dimensional reduction and theoretical analysis method.The results demonstrate that social and nonlinear interactions play an important role in modulating the directional switching behavior of pigeon focks.Specifically,increasing group density and the mean degree of the network can suppress the directional switching behavior.However,the influence of nonlinear parameters on directional switches is non-monotonic.Specifically,when the nonlinear parameter is small,an increase in its value tends to suppress directional switching behavior,while further augmentation can facilitate such direction switches.The augmentation of nonlinear parameters causes transitions from ordered to disordered directional switches within pigeon flocks.The research findings reveal the mechanisms of social and nonlinear interactions on the directional switches in pigeon focks,thereby providing a theoretical basis for

关 键 词：非线性相互作用 社交网络 方向切换行为 稳态概率密度 平均切换时间 

分 类 号：O157.5[理学—数学] Q95-33[理学—基础数学]