Search Theory is the field which deals with maximizing the detection of one or more targets, by optimizing the placement of detection resources. The optimization becomes particularly uneasy for moving targets, since it involves the full detection history. Combinatorial approaches are used for a small number of resources. For numerous resources, a continuous approach has been introduced by B.O. Koopman. And the resource optimization has been solved, for a target with a Markovian probabilistic prior. However, the evolution in time and the interactions of the resources remain difficult. Starting...