The purpose of the present study is to explain and describe (with the help of the probabilistic model) the process of breaking the stage of synchronous behavior and the emergence of a section of asynchronous dynamics in the regime of intermittent generalized chaotic synchronization in one-dimensional dynamical systems with discrete time.

Methods. In this paper, a probabilistic model is used to quantitatively describe the observed characteristics of the behavior of two unidirectionally coupled systems being near the onset of the synchronous regime.

Results. An analytical expression for the probability to observe the destruction of the synchronous phase on an interval of fixed duration under the assumption of uniformly distributed variable, as well as the form of the probability density function of the system state for the destruction intervals of synchronous dynamics are obtained.

Conclusion. The paper presents quantitative estimates of the process of destruction of synchronous behavior in the regime of intermittent generalized chaotic synchronization for one-dimensional dynamical systems with discrete time. The generality of processes near the boundary of the synchronous motion for generalized chaotic synchronization and noise-induced synchronization is shown.