Random search processes on complex networks: From a static target to a moving object

Abstract

We investigate the transition behavior of search time from visiting a static target to hunting a moving one on complex networks. This is achieved by introducing a relative moving speed ratio that quantifies how the time scale of a searcher differs from that of a mobile target. We adopt mean first encounter time to quantify the search time required to capture a time-moving target and derive its analytical expression. Remarkably, we find that with the increase of their relative speed ratio, the expected search time increases gradually and finally approaches that of visiting a static target. This interesting transition behavior keeps invariant even changing the associated navigation strategies of the searcher and the moving object. These findings are confirmed by numerical results on various synthetic and real networks. Our work, for the first time, reveals the increasing pattern of search time from a static target to a moving one on networks.