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In this paper, the global exponential synchronization of delayed complex dynamical networks with nonidentical nodes and stochastic perturbations is studied. By combining adaptive control and impulsive control schemes, the considered network can be synchronized onto any given goal dynamics. The adaptive control is discontinuous and can overcome the unknown difference between dynamical nodes and goal system. As for the impulsive control, the concept named “average impulsive interval” with “elasticity number” of impulsive sequence is utilized to get less conservative synchronization criterion. Numerical simulations are given to show the effectiveness and less conservativeness of the theoretical results.