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[en] This paper is to investigate the finite-time synchronization of stochastic Markovian jumping genetic oscillator networks with time-varying delay and Lévy noise. At first, we generalize the finite-time stability theorem from the systems driven by Brownian motion to the Markovian jumping systems with Lévy noise. And then, we utilize the stochastic Lyapunov functional method and appropriate control to obtain sufficient conditions for finite-time synchronization. Finally, two numerical examples are presented to verify the effectiveness of the proposed criteria.