Stability and synchronization of fractional-order delayed multilink complex networks with nonlinear hybrid couplings

In this paper, the stability and synchronization problems of fractional-order delayed multilink complex networks with nonlinear hybrid couplings are investigated simultaneously, where discrete time-varying delays and distributed time-varying delays are both taken into account. By virtue of graph-theoretic approach and Lyapunov method, under feedback control, some criteria are established to guarantee that the underlying networks achieve stability and synchronization. The obtained criteria are related to topological structure of subsystems, control gain, and the upper bound of time-varying delays. Furthermore, in order to show practicality, the obtained results are applied to fractional-order delayed multilink competitive neural networks with nonlinear hybrid couplings and fractional-order Lorenz chaotic delayed coupled systems with nonlinear hybrid couplings, respectively. Finally, two numerical examples are given to illustrate the effectiveness and feasibility of our theoretical results.