  We prove that cooperativity in Boolean networks precludes a strong notion of
sensitive dependence on initial conditions. Weaker notions of sensitive
dependence are shown to be consistent with cooperativity, but if each
regulatory functions is binary AND or binary OR, in N-dimensional networks they
impose an upper bound of approximately sqrt(3)^N on the lengths of attractors
that can be reached from a fraction p approaching 1 of initial conditions. The
upper bound is shown to be sharp.
