  The periodic swarming of bacteria is one of the simplest examples for pattern
formation produced by the self-organized collective behavior of a large number
of organisms. In the spectacular colonies of Proteus mirabilis (the most common
species exhibiting this type of growth) a series of concentric rings are
developed as the bacteria multiply and swarm following a scenario periodically
repeating itself. We have developed a theoretical description for this process
in order to get a deeper insight into some of the typical processes governing
the phenomena in systems of many interacting living units. All of our
theoretical results are in excellent quantitative agreement with the complete
set of available observations.
