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The relationship between the properties of a dynamical system and thestructure 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 areconstructed with the AND (resp. OR) operator only. The main results of thispaper describe network dynamics in terms of the structure of the networkdependency graph (topology). For a given such network, all possible limit cyclelengths are computed and lower and upper bounds for the number of cycles ofeach length are given. In particular, the exact number of fixed points isobtained. The bounds are in terms of structural features of the dependencygraph and its partially ordered set of strongly connected components. Fornetworks with strongly connected dependency graph, the exact cycle structure iscomputed.

The Dynamics of Conjunctive and Disjunctive Boolean Networks