Finite-Time Synchronization Of Competitive Neural Networks

In this paper, several issues will be investigated, including ?nite-time synchronization of competitive neural networks(CNNs) with(without) delays, synchronization of complex networks.Firstly, by traditional methods, ?nite-time lag synchronization of CNNs without delays was investigated, and several su?cient conditions for ?nite-time lag synchronization are obtained. Secondly, ?nite-time synchronization of competitive neural networks with discrete and distributed delays(mixed delays) will be studied, by introducing a suitable Lyapunov-Krasovskii’s function and utilizing analysis techniques, several su?cient conditions are obtained to ensure ?nite-time synchronization. Moreover, the setting time is explicitly given. Finally, we study synchronization of general complex networks with hybrid couplings and unknown perturbations, by designing a simple but all-powerful robust adaptive controller to synchronize the complex networks even without knowing bounds of the perturbations, and utilizing Lyapunov stability theory, integral inequality, Barbalat lemma and Schur Complement lemma, rigorous proofs are provided for synchronization of the complex networks. Numerical examples are given to verify the effectiveness of our theoretical result.