EXPONENTIAL STABILITY OF A MULTI-PARTICLE SYSTEM WITH LOCAL INTERACTION AND DISTRIBUTED DELAY  

作　　者：Yicheng LIU 刘易成(College of Liberal Arts and Sciences,National University of Defense Technology,Changsha 410073,China)

机构地区：[1]College of Liberal Arts and Sciences,National University of Defense Technology,Changsha 410073,China

出　　处：《Acta Mathematica Scientia》2022年第5期2165-2187,共23页数学物理学报（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(11671011).

摘　　要：For a collective system,the connectedness of the adjacency matrix plays a key role in making the system achieve its emergent feature,such as flocking or multi-clustering.In this paper,we study a nonsymmetric multi-particle system with a constant and local cut-off weight.A distributed communication delay is also introduced into both the velocity adjoint term and the cut-off weight.As a new observation,we show that the desired multi-particle system undergoes both flocking and clustering behaviors when the eigenvalue 1 of the adjacency matrix is semi-simple.In this case,the adjacency matrix may lose the connectedness.In particular,the number of clusters is discussed by using subspace analysis.In terms of results,for both the non-critical and general neighbourhood situations,some criteria of flocking and clustering emergence with an exponential convergent rate are established by the standard matrix analysis for when the delay is free.As a distributed delay is involved,the corresponding criteria are also found,and these small time lags do not change the emergent properties qualitatively,but alter the final value in a nonlinear way.Consequently,some previous works[14]are extended.

关 键 词：semi-simple eigenvalue flocking emergence clustering emergence distributed delay exponential convergence 

分 类 号：O19[理学—数学]