S-Asymptotically ω-Periodic Solutions of Fractional-Order Complex-Valued Recurrent Neural Networks With Delays

In this paper, we consider the problem of the S-asymptotically omega-periodic synchronization of fractional-order complex-valued recurrent neural networks with time delays. Firstly, we can not explicitly decompose the fractional-order complex-valued systems into equivalent fractional-order real-valued systems, by means of the contraction mapping principle and some important features of Mittag-Leffler functions, we obtain some sufficient conditions for the existence and uniqueness of S-asymptotically omega-periodic solutions for this class of neural networks. Then, by constructing an appropriate Lyapunov functional, the theory of fractional differential equation, and some inequality techniques, sufficient conditions are obtained to guarantee the global Mittag-Leffler synchronization of the drive-response systems. Finally, two examples are given to illustrate the effectiveness and feasibility of our main results.