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Dynamics of a coupled system of oscillator neurons is used for an area-wide signal control of an urban traffic network. Each signal is modeled by a simple phase oscillator with a periodic motion, and a pair-wise local interaction between the adjacent neurons leads to an entrainment with a phase difference which corresponds to a signal offset. Therefore, each pair-wise interaction is designed to attain a desired offset value. A coupling strength is given by a traffic flow density. Then, all offsets over the entire area are given by the global entrainment dynamics. In this paper, the method is applied to various traffic conditions including left or right turn traffic at an intersection and any number of crossing roads at an intersection. The results of computer simulations on several traffic flow patterns and conditions show the effective control by the statistics such as an average travel time.