  A cooperative network model of sociological interest is examined to determine
the sensitivity of the global dynamics to having a fraction of the members
behaving uncooperatively, that is, being in conflict with the majority. We
study a condition where in the absence of these uncooperative individuals, the
contrarians, the control parameter exceeds a critical value and the network is
frozen in a state of consensus. The network dynamics change with variations in
the percentage of contrarians, resulting in a balance between the value of the
control parameter and the percentage of those in conflict with the majority. We
show that the transmission of information from a network $B$ to a network $A$,
with a small fraction of lookout members in $A$ who adopt the behavior of $B$,
becomes maximal when both networks are assigned the same critical percentage of
contrarians.
