A decentralized adaptive synchronization problem for a simple yet nontrivial discrete-time stochastic model of network dynamics is investigated, which also illustrates a general framework for a class of adaptive control problems for complex systems with uncertainties. To describe synchronization phenomena in noisy environments, several new definitions of synchronization for stochastic systems are given and applied in our model. In the framework proposed, we prove that in four different cases on local goals, including "deterministic tracking," "center-oriented tracking," " loose tracking," and " tight tracking," under mild conditions on noise sequence and communication limits, the agents in the considered model can achieve global synchronization in sense of mean by using local estimators and controllers based on a least-squares (LS) algorithm. These results show that agents in a complex system disturbed by noise with communication limits can autonomously achieve the global goal of synchronization by using local LS-based adaptive controllers while they are pursuing for their local goals.