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.