Fixed-time synchronization of fractional-order complex-valued delayed neural networks with discontinuous activation functions

This article concentrates on the fixed-time synchronization (FXTS) of fractional-order complex-valued delayed neural networks with discontinuous activation functions. On the basis of the nonsmooth analysis, differential inclusion theory, Lyapunov stability theorem and complex function theory, some sufficient conditions are developed to guarantee the FXTS of such system by designing a novel fractional-order complex-valued controller. The fixed-time synchronization can make up the limitation of the previous finite-time synchronization results, that is, fixed-time synchronization time relies on the parameters of controller, which is independent of initial values. Additionally, the upper limit of synchronization time is estimated accurately. Furthermore, our results improve some finite-time synchronization and fixed-time synchronization ones. Finally, the effectiveness of theoretical results is demonstrated by some numerical simulations.