Synchronization with general decay rate for memristor-based BAM neural networks with distributed delays and discontinuous activation functions

Meng Yan a , b , Ming hui Jiang a , b , ∗

Abstract：In this paper, we investigate the general decay synchronization (GDS) of memristor-based BAM neural networks (MBAMNNs) with mixed time delays as well as discontinuous activations. First, the concept of the Filippov solution is extended to functional differential equations with discontinuous right-hand sides via functional differential inclusions. Then, by constructing suitable Lyapunov-krasovskii functionals and employing some useful inequality techniques, several novel conditions ensuring the GDS of considered BAM neural networks are obtained through designing two different types of nonlinear controllers. The results we proposed in this paper are general since GDS have generalized the traditional asymptotical synchronization, exponential synchronization, polynomial synchronization and contained them as its special cases. Finally, two examples and their numerical simulations are provided to demonstrate the effectiveness of our theoretical results.