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The fractional-order Belousov-Zhabotinsky (BZ) reaction with different time scales is investigated in this paper. Based on the stability theory of fractional-order differential equation, the critical condition of Hopf bifurcation with two parameters in fractional-order BZ reaction is discussed. By comparison of the fractional-order and integer-order systems, it is found that they will behave in different stabilities under some parameter intervals, and the parameter intervals may become larger with the variation of fractional order. Furthermore, slow-fast effect is firstly studied in fractional-order BZ reaction with two time scales coupled, and the Fold/Fold type slow-fast oscillation with jumping behavior is found, whose generation mechanism is explained by using the slow-fast dynamical analysis method. The influences of different fractional orders on the slow-fast oscillation behavior as well as the internal mechanism are both analyzed.

Stability and slow-fast oscillation in fractional-order Belousov-Zhabotinsky reaction with two time scales