Distributed adaptive finite-time and fixed-time cluster synchronization of complex networks

This paper aims to study the finite-time (FNT) and fixed-time (FXT) cluster synchronization problems of complex networks (CNs). First, to ensure scalability of CNs, the adaptive laws are proposed to update coupling weights between neighboring nodes in same cluster. In this case, only local information is required instead of global one. Then, by designing the appropriate controllers and employing Lyapunov stable theory, several sufficient conditions are obtained to fulfill cluster synchronization in FNT and FXT. When the number of clusters is single, the general FNT and FXT synchronization are also investigated under distributed adaptive strategies. Finally, the theoretical results are verified by a numerical simulation example.