Asymptotic behavior of some linear differential systems

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:144

Article

Chiang, TS ; Chow, YS

关键词: linear differential systems;    asymptotic behavior;    cycle method;   

DOI  :  10.1006/jdeq.1997.3382

来源: Elsevier

【 摘 要 】

Consider the following chasing game in R among b particles whose trajectories are governed by the following differential equations: For i is an element of S = {1, 2,..., b}, F-i' = Sigma(j not equal i) q(ij)(t)(F-j(t)-F-i(t)), where F-i(t) is the position at time i of the particle i and q(ij)(t), which measures the instantaneous rate that particle i is attracted toward particle j, is given by q(ij)(t) = p(ij)lambda(t)(U(i,j)) for j not equal i. The rate function lambda(t) is positive with lim(i-->infinity) lambda(t) = 0, U(i, j)is an element of [0, infinity] is the cost function indicating the level of difficulty from i not equal j and the nonnegative numbers p(ij) for i not equal j reflect the neighborhood structure of the particles. Particles are attracted to one another but such attraction becomes weaker as lime goes on. A sufficient condition on lambda(t) is given for all F-i(t) converging to a common finite limit. (C) 1998 Academic Press.

【 授权许可】

Free