Fig. 1. Relation between the order parameter ((a), (b)) and the coupling strength K. Arrows denote the direction of the adiabatic change of the coupling K: (a) ; (b) .

Fig. 2. (a) curves when ; (b) the intersection of curves and for different couplings K, where , , .

Fig. 3. The order parameters [(a)—(c)] and [(d)—(f)] varying against the coupling strength K for different γ and , when the natural frequency obeys a bimodal Lorentz distribution: (a), (d) ; (b), (e) ; (c), (f) . Theoretical predictions and numerical results are labeled as solid lines and symbols, respectively ( ). For every η, the initial phase is set as 0 and π for η and 1–η.

Fig. 4. Oscillatory behaviors of the order parameter for different coupling strengths K, where , , , and : (a), (b) ; (c), (d) .

Fig. 5. curves where 2m is the number of peaks of the distribution function for .

Fig. 6. The order parameters [(a), (c)] and [(b), (d)] varying against the coupling strength K for different m and : (a), (b) ; (c), (d) . Theoretical predictions and numerical results are labeled as solid lines and symbols, respectively. The dotted lines are the theoretical predictions of the critical values of ADT given in (40).