Finite-time synchronization of a class of nonlinear complex-valued networks with time-varying delays

This paper focuses on the problem of finite-time synchronization for a class of nonlinear complex-valued networks with time-varying delays. A novel model is proposed to generalize the previous works. The nonlinear couplings, time-varying node delay and multiple time-varying coupling delays are considered; all the variables and parameters in this model are considered as complex values. By decomposing the network model to real and imaginary parts, an equivalent real-valued system is built. Then, by utilizing the linear feedback controllers, synchronization is achieved in a given finite time rather than merely asymptotically synchronize. Based on the finite-time stability theory, Lyapunov functional method and some mathematical analysis techniques, sufficient conditions are strictly established to ensure the finite-time synchronization, the main results can be also extended to the networks without node delay or coupling delays. At last, examples are provided in details to demonstrate our results. (C) 2019 Elsevier B.V. All rights reserved.