相位振荡器系统的长时间演化
Long Time Evolution of Phase Oscillator Systems
摘要：
它示出，在较弱的条件下，一类重要的大系统的全球耦合，异质频率，相位振荡器的动态演化，在适当的物理意义上，时间渐近吸引到一个减少的系统状态的流形。这个流形在系统演化下是不变的，以前是已知的，并用于促进发现吸引子和分叉。本文的结果表明，通过限制到这个简化流形上得到的序参量动力学的吸引子实际上是整个系统唯一的吸引子。这样，通过对约化流形的约束，可以得到这些系统的序参量的所有长时间动力学行为。
英文摘要：
It is shown, under weak conditions, that the dynamical evolution of an important class of large systems of globally coupled, heterogeneous frequency, phase oscillators is, in an appropriate physical sense, time-asymptotically attracted toward a reduced manifold of system states. This manifold, which is invariant under the system evolution, was previously known and used to facilitate the discovery of attractors and bifurcations of such systems. The result of this paper establishes that attractors for the order parameter dynamics obtained by restriction to this reduced manifold are, in fact, the only such attractors of the full system. Thus all long time dynamical behavior of the order parameters of these systems can be obtained by restriction to the reduced manifold.
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