We consider the problem, of tracking visually identifiable mobile targets using a distributed system of mobile robots. We propose a behavior-based approach where mobile robots with limited sensory range use a search pattern obsewed in nature - the Levy distributed search, to locate a mobile target. The Levy search pattern is inspired by the foraging pattern exhibited by social insects such as honeybees, albatrosses, etc. We consider two Levy-distributed search patterns - a Levy timed search and a Levy looped search, and determine their performance in locating and tracking mobile as well as stationary targets. Our results show that for locating stationary targets, the Levy length for a search leg is strongly correlated with the distance of the target from the location where the search starts. For locating and tracking mobile targets, we find that the search performance improves as the p.d.f. of the Levy distribution is made flatter. The Levy looped search also performs better than the Levy timed search in tracking mobile targets because its looping property helps in relocating targets that have been observed previously.