  This paper presents the notion of stochastic phase-cohesiveness based on the
concept of recurrent Markov chains and studies the conditions under which a
discrete-time stochastic Kuramoto model is phase-cohesive. It is assumed that
the exogenous frequencies of the oscillators are combined with random variables
representing uncertainties. A bidirectional tree network is considered such
that each oscillator is coupled to its neighbors with a coupling law which
depends on its own noisy exogenous frequency. In addition, an undirected tree
network is studied. For both cases, a sufficient condition for the common
coupling strength and a necessary condition for the sampling-period are derived
such that the stochastic phase-cohesiveness is achieved. The analysis is
performed within the stochastic systems framework and validated by means of
numerical simulations.
