  The dynamics of one-way coupled systems with discrete time is considered. The
behavior of the coupled logistic maps is compared to the dynamics of maps
obtained using the Poincare sectioning procedure applied to the coupled
continuous-time systems in the phase synchronization regime. The behavior
(previously considered as asynchronous) of the coupled maps that appears when
the complete synchronization regime is broken as the coupling parameter
decreases, corresponds to the phase synchronization of flow systems, and should
be considered as a synchronous regime. A quantitative measure of the degree of
synchronism for the interacting systems with discrete time is proposed.
