  An important problem in the theory of finite dynamical systems is to link the
structure of a system with its dynamics. This paper contains such a link for a
family of nonlinear systems over the field with two elements. For systems that
can be described by monomials (including Boolean AND systems), one can obtain
information about the limit cycle structure from the structure of the
monomials. In particular, the paper contains a sufficient condition for a
monomial system to have only fixed points as limit cycles. This condition
depends on the cycle structure of the dependency graph of the system and can be
verified in polynomial time.
