A collective motion algorithm for tracking time-dependent boundaries

We present a numerical method that allows a formation of communicating agents to target the boundary of a time-dependent concentration by following a time-dependent concentration gradient. The algorithm motivated by [3,1], allows the agents to move in space in a non-stationary environment. Our method is applicable to finding the boundary of any regular surface and may be of interest for studying motions of swarms in biology, as well as to engineering applications where boundary detection is an issue.