Abstract In this paper, we investigate numerically the chaotic behaviours in the fractional-order Genesio--Tesi system. We find that chaos exists in the fractional-order Genesio--Tesi system with order less than 3. The lowest order we find to have chaos is 2.4 in this fractional-order Genesio--Tesi system. We propose a drive-response synchronization method for synchronizing the fractional-order chaotic Genesio--Tesi systems only using a scalar drive signal. This synchronization approach, based on stability theory of fractional-order systems, is simple and theoretically rigorous. It does not require the computation of the conditional Lyapunov exponents.Simulation results are used to visualize and illustrate the effectiveness of the proposed synchronization method.
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