Phase synchronization degree r as a function of the coupling strength C for different δ in a BA scale-free network (left panels) and a ER random network (right panels). (a) and (d) for , (b) and (e) for , and (c) and (f) for . Squares (circles) in (a)–(f) mark the forward (backward) simulations, as C is increased (decreased) in steps of . Other parameters are N = 200, , and the average degree .
Area of hysteresis loop in the synchronization diagram of BA scale-free networks as a function of δ. Other parameters are the same as Fig. 1 .
The average frequencies for different degrees k along the forward simulation. (a) BA networks: ; (b) BA networks: ; (c) ER networks: . The arrows in (a)–(c) indicate the decreasing order of degrees. Other parameters are the same as Fig. 1 .
Area of hysteresis loop in synchronization diagram of BA networks as a function of noise intensity Dy for (a) and as a function of Dx for (b). and other parameters are the same as Fig. 1 .
Synchronization diagram in BA scale-free networks without any correlation and with the negative correlation between degrees and natural frequencies. Other parameters are the same as Fig. 1 .
Effect of degree-degree correlations on the property of the synchronization transition. (a) Synchronization diagram at for different degree-mixing coefficients rk . (b) Area of hysteresis loop in synchronization diagram as a function of δ for different rk . (black squares), (red circles), (green triangles), and (blue diamonds). Other parameters are the same as Fig. 1 .
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