Quasi-synchronization for fractional-order delayed dynamical networks with heterogeneous nodes

This paper investigates the quasi-synchronization problem in heterogeneous fractional order dynamic networks with time-delay. Based on comparison theorem for the fractional order differential equation, a new fractional order functional differential inequality is built at first. According to the inequality, some quasi-synchronization conditions are derived via Lyapunov method, and the error bound is estimated. Then, the pinning control strategy is also considered via matrix analysis. Furthermore, the specific pinning schemes about how many nodes are needed to be selected are provided in an algorithm. Finally, two examples are given to verify the validity of our theoretical results.