Observer-based aperiodically intermittent pinning synchronization of complex-valued dynamical networks with time-varying delay

This paper addresses the impact of time delay and unavailability of system states on synchronization in complex networks. Specifically, it focuses on observer -based synchronization of complex -valued dynamical networks (CDNs) with time -varying delays, encompassing both complex -valued node dynamics and outer coupling forms. Two aperiodically intermittent control schemes, with and without pins, are proposed to reduce control costs by minimizing control frequency and the number of controllers. The proposed schemes establish sufficient criteria for guaranteeing synchronization in CDNs with time -varying delays, utilizing a combination of Lyapunov function and inequality technology in the complex field. Numerical examples are provided to illustrate the effectiveness of the proposed theoretical results.