带有一般非线性结构的觅食群体的稳定性分析  

Stability Analysis of Foraging Swarms with General Nonlinear Structure

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作  者:杨丽艳[1] 郑毓蕃[1,2] 

机构地区:[1]上海大学数学系,上海200444 [2]华东师范大学数学系,上海200062

出  处:《复杂系统与复杂性科学》2009年第2期10-18,共9页Complex Systems and Complexity Science

基  金:国家自然科学基金(60674046)

摘  要:在二维欧氏空间中,研究满足单峰函数性质的外部源(营养/有毒)环境下一类带有吸引和排斥结构的觅食群体的行为。仅假定群体成员间具有一般的非线性吸引和排斥性质。分析说明群体整体行为的涌现是群体成员之间的相互作用以及群体与外部环境作用平衡的结果。表明对称联通群体的所有成员会根据不同性质的源(营养或有毒)朝着或远离该区域聚集,并形成大小有限的聚集群。此外,对吸引和排斥函数作适当的假设,证明群体是编队稳定的。This paper studies a class of foraging swarms with general nonlinear attraction and repulsion structure under a nutrient/toxic profile which is of unimodal property in 2-dimensional space. In this work the interaction among agents is of general nonlinear attraction/repulsion property. It is illustrated that the emergent behavior of the swarms in this type is the result of a balance between the interactions among swarm members as well as the interactions of the swarm with its environment. It is shown that the agents of the reciprocal swarm with connective network will aggregate and eventually form a cohesive cluster of finite size moving toward or away from the area depending on different profile (nutrient or toxic). Furthermore, under some mild assumptions on attraction and repulsion functions, we prove that the swarm is formation stable.

关 键 词:群体 吸引和排斥函数  非线性系统 

分 类 号:O23[理学—运筹学与控制论] N94[理学—数学]

 

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