  The "theory of open sub-functorial dynamics" is a new theory that defines
interacting generalized dynamical systems. The interactions between these
dynamics produce new dynamics which, of course, can then enter into other
interactions. A major part of this article can already be found in two
unpublished texts and it has been partially exposed in conferences. However, we
need to give a new, unified and therefore more convenient presentation of this
material, and we also need some examples to illustrate it. Moreover, we
introduce in this article the new concepts of "normal interaction" and
"concrete interaction", and replace the previously used rigid synchronizations
by much more general flexible ones.
