  The relationship between the properties of a dynamical system and the
structure of its defining equations has long been studied in many contexts.
Here we study this problem for the class of conjunctive (resp. disjunctive)
Boolean networks, that is, Boolean networks in which all Boolean functions are
constructed with the AND (resp. OR) operator only. The main results of this
paper describe network dynamics in terms of the structure of the network
dependency graph (topology). For a given such network, all possible limit cycle
lengths are computed and lower and upper bounds for the number of cycles of
each length are given. In particular, the exact number of fixed points is
obtained. The bounds are in terms of structural features of the dependency
graph and its partially ordered set of strongly connected components. For
networks with strongly connected dependency graph, the exact cycle structure is
computed.
