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Without assuming that the communication topology can remain its connectivity frequently enough and the potential function can provide an infinite force during the evolution of agents, the flocking problem of multi-agent systems with second-order non-linear dynamics is investigated in this study. By combining the ideas of collective potential functions and velocity consensus, a connectivity-preserving flocking algorithm with bounded potential function is proposed. Using tools from the algebraic graph theory and matrix analysis, it is proved that the designed algorithm can guarantee the group of multiple agents to asymptotically move with the same velocity while preserving the network connectivity if the coupling strength of the velocity consensus term is larger than a threshold value. Furthermore, the flocking algorithm is extended to solve the flocking problem of multi-agent systems with a dynamical virtual leader by adding a navigation feedback term. In this case, each informed agent only has partial velocity information about the leader, yet the present algorithm not only can guarantee the velocity of the whole group to track that of the leader asymptotically, and also can preserve the network connectivity. Finally, some numerical simulations are provided to illustrate the theoretical results.