Synchronization analysis of linearly coupled delayed neural networks with discontinuous activations

In this study, without assuming the symmetry or irreducibility of the coupling configuration matrix, we investigate the synchronization of linearly coupled dynamical systems with discontinuous identical nodes and time delay. First, we design a feedback controller to realize the complete synchronization and exponential synchronization of discontinuous complex networks using a generalized Lyapunov approach. Second, we propose a set of adaptive controllers and adaptive laws to achieve complete synchronization. Third, we study the adaptive pinning synchronization of the discontinuous complex networks. The results of numerical simulations are presented to demonstrate the effectiveness of the controllers and the correctness of the theoretical results.