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In this paper, we investigate the finite flocking problem of Cucker-Smale systems. We propose a continuous non-Lipschitz protocol for realizing flocking in finite time. Both our theoretical and numerical results uncover a power-law relationship between the convergence time and the number of individuals. Our results show that the individuals in groups with high density can transit rapidly to ordered collective motion.

In this paper, we study the complete synchronization between two chaotic systems with on–off periodic coupling. Using the stability theory and the comparison theorem of differential equations, we derive less restrictive synchronization conditions than those resulting from the Lyapunov theory. The theoretical results show that two chaotic systems can achieve complete synchronization if the time-average coupling strength is large enough. Finally, numerical simulations fully verify the effectiveness of the analytical results.