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Note that the splitting (desynchronizing) force depends on not only Kχ but also c2. Since the dispersion of the effective natural frequencies is proportional to c2 , increasing c2 will intensify the force and hence enhance the inhomogeneity of the system. This explains why the value of σ grows as c2 is increased, as seen in Fig. 7. Although the value of Kχ tends to decrease for increasing c2 (see the inset of Fig. 7), such a change is relatively small and hence does not affect the behavior of σ in a qualitative way.
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Note that the splitting (desynchronizing) force depends on not only Kχ but also c2. Since the dispersion of the effective natural frequencies is proportional to c2, increasing c2 will intensify the force and hence enhance the inhomogeneity of the system. This explains why the value of σ grows as c2 is increased, as seen in Fig. 7. Although the value of Kχ tends to decrease for increasing c2 (see the inset of Fig. 7), such a change is relatively small and hence does not affect the behavior of σ in a qualitative way.
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This sticking of oscillator trajectories to the incoherent circle, which is enhanced by increasing c2 , provides a possible reason why the peak of σ shifts to the small K side as c2 grows, as Fig. 7 indicates. This is because in the limit of strong sticking, σ should be approximated by rIC = 1-K and hence become maximum near K=0.
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This sticking of oscillator trajectories to the incoherent circle, which is enhanced by increasing c2, provides a possible reason why the peak of σ shifts to the small K side as c2 grows, as Fig. 7 indicates. This is because in the limit of strong sticking, σ should be approximated by rIC = 1-K and hence become maximum near K=0.
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This may imply that the scaling law of an order parameter proposed in our earlier paper does not hold over a full range of the scaling variable, since it is based on the assumption that both the active and inactive groups are synchronized. However, the scaling law is about a close vicinity of the critical point, where the horn is quite thin, unless the nonisochronicity of oscillators is extremely strong. One can therefore expect that it practically holds even if a desynchronization horn exits. Of course, if the stably coexisting synchronized state is traced from outside the horn, then no violation of the scaling law will occur at all.
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This may imply that the scaling law of an order parameter proposed in our earlier paper does not hold over a full range of the scaling variable, since it is based on the assumption that both the active and inactive groups are synchronized. However, the scaling law is about a close vicinity of the critical point, where the horn is quite thin, unless the nonisochronicity of oscillators is extremely strong. One can therefore expect that it practically holds even if a desynchronization horn exits. Of course, if the stably coexisting synchronized state is traced from outside the horn, then no violation of the scaling law will occur at all.
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