General decay synchronization stability for a class of delayed chaotic neural networks with discontinuous activations

•A new crucial lemma which concerns stability in general decay rate is constructed.•General decay synchronization stability criteria of neural networks with discontinuous activations are derived.•The general decay synchronization contains exponential and polynomial synchronization as its two special cases.•Complete synchronization of the discontinuous neural networks can be achieved via the designed controller.•The results of this paper are general and can be applied to continuous or discontinuous delayed nonlinear systems.

This paper is concerned with the synchronization problem for a class of delayed chaotic neural networks with discontinuous activations. First a lemma which concerns stability in general decay rate is constructed. Based on this lemma, the general decay synchronization stability criteria of discontinuous neural networks are derived via a designed controller. The general decay synchronization is obtained by introducing a decay function and it contains exponential synchronization and polynomial synchronization as its two special cases. Finally, two examples are given to verify the effectiveness of the obtained results.