We report an investigation of the processes of search, identification, and visual tracking of specified individual moving objects and groups of moving objects with different or identical geometric shapes that appear, move, and vanish randomly against the background of other moving objects not specified by instructions and exhibit similar behaviors on a screen simulating the indicator of a surveillance radar system. The aim of this study is to determine the limits on the number of moving objects that are simultaneously recognized and tracked by the operator against the background of other objects. Investigations on the detection and analysis of areas where operators focus their attention in the process of tracking the trajectories of movement of the specified objects and groups are carried out. The appearance of dynamic areas of attention under the specified conditions is established. The capacity of such areas is not more than 3-4 simultaneously tracked dynamic objects and does not depend on their shape, movement pattern, and presence of other moving objects with similar properties. (C) 2021 Optical Society of America