How a Searcher Catches a Mobile Target with Different Relative Velocities on Complex Networks

We focus on a question how the search time varies when a searcher and a target take different speeds moving on the networks. We first define the relative velocity ratio between them as [Formula: see text]. Then we use the mean first encounter time (MFET) to quantify the search time, and derive its analytical expressions from a simple case (i.e., [Formula: see text]) to more general case (i.e., [Formula: see text]). We consider two typical examples where both searcher and target adopt unbiased random walk (URW) strategy and maximal entropy random walk (MERW) strategy, respectively. Both strategies present a similar variation trend on the real and synthetic networks where the search time keeps increasing till it approaches the mean first passage time in the static target case. With comparison, we also find the MERW strategy is more efficient when [Formula: see text] is relatively small, while URW strategy gradually outperforms MERW with the growth of [Formula: see text].