  Here we analyze the behavior of dynamically coupled maps, based on those
introduced in a series of papers by Ito and Kaneko (Phys. Rev. Lett. 88:028701,
2002 and Phys. Rev. E 67:046226, 2003). We show how the microscopic coupling
mechanism changes the behavior of the system both by affecting the stability of
fixed points and through a more subtle effect in the crossover behavior between
different regions of the parameter space. This makes it necessary to choose
very carefully the exact manner in which one couples maps if they are to be
used as a general model of composite systems.
