New results of quasi-projective synchronization for fractional-order complex-valued neural networks with leakage and discrete delays

In this paper, the non-decomposition method is employed to investigate the quasi-projective synchronization of fractional-order complex-valued neural networks (FOCVNNs) with leakage and discrete delays. Firstly, two new inequalities are established in complex domain, which provides a powerful tool to explore the synchronization and stability of complex-valued systems. Secondly, by means of the Banach fixed point theorem, the existence and uniqueness of solution of the delayed FOCVNNs is discussed under certain conditions. Thirdly, a linear complex-valued controller is designed to induce quasi-projective synchronization of the delayed FOCVNNs, and some novel results are given by using the presented inequalities, the non-decomposition method and the Lyapunov stability theory. Further, the error bounds are estimated. It is found that a smaller error bound can be obtained by appropriately increasing the feedback gains. Finally, two numerical examples are given to verify the effectiveness of the theoretical results and the practicability of the synchronization strategy in secure communication.