Synchronization Of Two Classes Of Delayed Chaotical Systems With Uncertain Nonlinear Perturbations

The issue of synchronization for two chaotical systems are studied. The one is timedelayed neural networks with discontinuous activations, and the other one is hybrid coupled(discrete couple and distributed couple) complex networks with mixed delays(discrete delay and distributed delay) and unknown non-stochastic external perturbations.Due to the time-delay, most of existing methods for ?nite-time synchronization of non-delayed systems can not be applied to the delayed neural networks. A simple controller and a new Lyapunov-Krasovskii functional are designed to study ?nite-time synchronization of time-delayed neural networks with discontinuous activations. Su?cient conditions of guaranteeing ?nite-time synchronization of the neural networks are obtained.Because continuity is a special situation of discontinuity, the corresponding results also can be applied to the continuous neural networks.On the other hand, a issue of synchronization for a class of hybrid coupled complex networks with mixed delays and unknown non-stochastic external perturbations is also studied. To overcome the bad effects of perturbations, a robust adaptive controller is designed to synchronize the complex networks. Basing on Lyapunov stability theory,integral inequality, Barbalat lemma and Schur Complement lemma, rigorous proofs are given for synchronization of the complex networks. Numerical simulations verify the effectiveness of the new robust adaptive controller.