This paper mainly studies the finite time synchronization problem of stochastic multi weights complex network model with time-varying delay. First, the multi weights complex network model was established, which includes Lévy noise and coupled time-varying delay. Second, by designing continuous control strategy, the new criterion for finite time synchronization of multi weights complex network model driven by Lévy noise was discussed with inequalities and Lyapunov theory. Finally, the effectiveness of the theoretical results was verified through two numerical examples. The results show that as the connection weights between nodes increase, the interaction between nodes is enhanced, which helps the network reach synchronization faster. Time-varying delay and Lévy noise can lead to the decrease in network synchronization quality, which is caused by increasing synchronization errors or extending synchronization time.
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