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Coupled oscillator models provide an essential theoretical framework for modeling various biological networks and analyzing their collective behavior, such as synchronization and clusters formation. These simple models often miss internal and external disturbances. Therefore, a stochastic approach provides a significant compromise to keep modeling complexity tractable and still capture important phenomena. In this talk, we study a noisy network of coupled oscillators in the sense that each oscillator is driven by two sources of state-dependent noise: (1) an intrinsic noise which is common among all oscillators and can be generated by the environment or any internal fluctuations, and (2) a noisy coupling which is generated by interactions with other oscillators. Our goal is to understand the effect of noise and coupling on synchronization behaviors of the network and time period of each oscillator. To this end, we first provide sufficient conditions that foster synchronization in noisy networks of general systems. Then, we focus on a noisy network of weakly coupled oscillators, derive its coupled phase equations by the notion of first- and second-order phase response curves (PRCs), and find synchronization conditions based on the PRCs. Finally, using the first passage time and Fokker-Planck equations, we compute mean and variance of the time period of synchronization solutions and compare them with the time period of isolated oscillators.