Synchronization analysis of fractional delayed dynamical networks under switching topology

Abstract This article addresses the global synchronization of fractional dynamical networks with both delayed and non-delayed couplings under a switching topology, where the coupling configuration matrices need not be commutative. By utilizing a modified fractional Razumikhin technique, the common Lyapunov function method and graph theory, we present a convenient and effective approach to establish reliable algebraic criteria for global synchronization. Our method effectively overcomes the challenges associated with fractional calculus, time delays, and switching topologies. A key finding is that global synchronization can be achieved more rapidly by adding additional edges to the coupling configuration graphs. Additionally, an illustrative example is provided to demonstrate the effectiveness of our theoretical results.