AI 中文总结
该研究探究了频率加权Kuramoto振子双谐波耦合的集体动力学，构建了相图，揭示了三种集体态及转变特性，理论与数值结果吻合良好。
AI 中文摘要
我们研究了具有频率加权双谐波耦合的全局耦合相位振子的集体动力学。尽管Kuramoto模型的频率加权扩展和双谐波扩展已被分别研究，但它们的组合效应仍未被探索。通过结合数值分支延拓与解析稳定性分析，我们在双参数耦合平面中构建了完整的相图。一次谐波与二次谐波相互作用之间的竞争产生了三种不同的集体态：非相干态（IC）、对跖多分支态（APMS）和对称破缺多分支态（SBMS）。这些态被三个双稳区域和一个狭窄的三稳区域分隔，在三稳区域中所有三个态作为稳定吸引子共存。从非相干态向两种有序态的转变是不连续且具有滞后性的，反映了由频率加权诱导的爆炸同步，而APMS与SBMS之间的转变也是突变的。在解析上，我们推导了非相干态的线性不稳定性阈值以及SBMS的存在性和局部稳定性条件，结果表明理论预测与大量数值模拟吻合良好。
英文摘要
We investigate the collective dynamics of globally coupled phase oscillators with frequency-weighted biharmonic coupling. Although frequency-weighted and biharmonic extensions of the Kuramoto model have each been studied independently, their combined effect has remained unexplored. By combining numerical branch continuation with analytical stability analysis, we construct the complete phase diagram in the two-parameter coupling plane. The competition between the first- and second-harmonic interactions gives rise to three distinct collective states: the incoherent state (IC), the antipodal multibranch state (APMS), and the symmetry-broken multibranch state (SBMS). These states are separated by three bistable regions and a narrow tristable region in which all three states coexist as stable attractors. The transitions from the incoherent state to both ordered states are discontinuous and hysteretic, reflecting the explosive synchronization induced by frequency weighting, while the transition between the APMS and SBMS is also abrupt. Analytically, we derive the linear instability thresholds of the incoherent state together with the existence and local stability conditions for the SBMS, and show that the theoretical predictions are in good agreement with extensive numerical simulations.
Comments11 pages, 7 Figures
