Asymptotic and finite-time synchronization of fractional-order multiplex networks with time delays by adaptive and impulsive control

Abstract

In this article, we analyze the asymptotic synchronization of fractional-order multiplex networks with time delays via adaptive control, where intra-layer and inter-layer transmission delays are taken into consideration. By introducing a new fractional-order Halanay-type inequality and utilizing graph-theoretic method and Lyapunov method, we formulate some sufficient conditions to ensure the asymptotic synchronization of fractional-order multiplex networks with time delays. Furthermore, in the case that there is no delay in intra-layer and inter-layer transmissions, we investigate the finite-time synchronization of fractional-order multiplex networks by impulsive control. Meanwhile, the upper bound of the settling time for finite-time synchronization is reckoned. In addition, the results herein are applied to coupled Chua’s circuits on fractional-order multiplex networks with time delays. Finally, some numerical simulations are carried out to demonstrate the effectiveness of the developed results.