自洽方法与二阶振子的稳态
Self-consistent Method and Steady States of Second-order Oscillators
摘要：
自洽方法是由Kuramoto首先提出的，它是分析耦合振子网络稳态的有力工具。对于二阶振子网络，由于稳定不动点和稳定极限环的共同存在而导致的混沌行为，以及相应的吸引域之间的复杂边界，使得自洽方法的应用变得复杂。在本文中，我们报告的二阶振荡器的自洽分析，这是比较简单的，而以前的方法，同时给出更准确的结果，在小惯性制度和接近不相干。我们应用该方法分析了耦合二阶振子的稳态，并引入了裕度域和标度惯量的概念。接近不相干的自洽方法的改进的准确性导致从不相干的过渡对应的临界耦合的准确估计。
英文摘要：
The self-consistent method, first introduced by Kuramoto, is a powerful tool for the analysis of the steady states of coupled oscillator networks. For second-order oscillator networks complications to the application of the self-consistent method arise because of the bistable behavior due to the co-existence of a stable fixed point and a stable limit cycle, and the resulting complicated boundary between the corresponding basins of attraction. In this paper, we report on a self-consistent analysis of second-order oscillators which is simpler compared to previous approaches while giving more accurate results in the small inertia regime and close to incoherence. We apply the method to analyze the steady states of coupled second-order oscillators and we introduce the concepts of margin region and scaled inertia. The improved accuracy of the self-consistent method close to incoherence leads to an accurate estimate of the critical coupling corresponding to transitions from incoherence.
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