New μ-Synchronization Criteria for Nonlinear Drive–Response Complex Networks with Uncertain Inner Couplings and Variable Delays of Unknown Bounds

Since the research of μ-synchronization helps to explore how complex networks (CNs) work together to produce complex behaviors, the μ-synchronization task for uncertain time-delayed CNs is studied in our work. Especially, bounded external perturbations and variable delays of unknown bounds containing coupling delays, internal delays, and pulse delays are all taken into consideration, making the model more general. Through the μ-stable theory together with the hybrid impulsive control technique, the problems caused by uncertain inner couplings, time-varying delays, and perturbations can be solved, and novel synchronization criteria are gained for the μ-synchronization of the considered CNs. Different from traditional models, it is not necessary for the coupling matrices to meet the zero-row-sum condition, and the control protocol relaxes the constraint of time delays on impulse intervals. Moreover, numerical experiments and image encryption algorithms are carried out to verify our theoretical results’ effectiveness.