This paper focuses on network-based master-slave synchronization for delayed neural networks through a remote controller. The insertion of communication networks in a master-slave synchronization scheme inevitably induces network delays, packet dropouts and stochastic fluctuations. The data packets may be received with a different temporal order from that they are sent due to the fact that the network-induced delay is time-varying. A logic data processor and a logic zero order hold are proposed in the master-slave synchronization framework. Then an error system for the master system and the slave system is formulated. By combining a generalized Jensen integral inequality and a convex combination technique, some synchronization criteria are derived to ensure the mean-square global exponential synchronization of state trajectories for the master system and the slave system. The controller gain matrix is obtained by solving a minimization problem in terms of linear matrix inequalities using a cone complementary technique. As a special case in which only network-induced delays and packet dropouts are occurred in the signal transmission channels, some results are also presented. Finally, two illustrative examples are provided to show the effectiveness and applicability of the proposed scheme.