Nonautonomous phenomenon occurs in

Nonautonomous phenomenon occurs in many realistic systems. Particularly, when we consider a long-time dynamical behavior of network, the parameters of the network usually change along with time and spatial position. Thus, it is important to study variable-coefficient complex dynamical networks with reaction-diffusion terms [2], [48]. During recent decades, researchers have studied extensively and systematically about variable-coefficient complex dynamical networks with reaction-diffusion terms and achieved fruitful results [2], [48]–​[51]. The dynamic phenomena cannot be simply determined by focusing on the individual elements. Hence, the dynamics depends on the properties of each individual unit, the nature of the interaction (couplings), and a wide range of different behaviors can be established by varying the coupling strength and structure of networks. Therefore, more and more researchers are devoted to the research of complex dynamical networks and its synchronization problems.