Phase- and Center-Manifold Reductions for Large Populations of Coupled Oscillators with Application to Non-Locally Coupled Systems
Phase- and Center-Manifold Reductions for Large Populations of Coupled Oscillators with Application to Non-Locally Coupled Systems
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大量耦合振荡器的相位流形和中心流形缩减及其在非局部耦合系统中的应用
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
Y. Kuramoto
中科院分区：
文献类型：
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作者：
Y. Kuramoto
在这篇文章的前半部分，我们将发展一些关于如何在数学上接近大的耦合极限环振荡器系统的一般思想。针对具有周期性活动的生物细胞组装原型系统，提出了两种具有代表性的还原技术，即相位还原和中心流形还原。根据振子耦合的范围，将每种约简方法导出的演化方程进一步分为三组（局部、全局和中间）。结果得到了六类模型方程。在本文的后半部分，我们将报道我们最近在非局部耦合振子研究中的一些新结果，并详细讨论服从幂律的反常湍流波动的产生。
In the first half of this paper, some general ideas will be developed on how to approach mathematically large systems of coupled limit-cycle oscillators. Two representative reduction techniques, namely, the phase reduction and the center-manifold reduction will be presented for a prototypal system of biological cell assembly with periodic activity. The evolution equation derived through each reduction method is further classified into three groups according to the range of the oscillator coupling (i.e. local, global and intermediate). As a consequence, six classes of model equations are obtained. In the second half of the paper, some new results from our recent study on non-locally coupled oscillators will be reported, and the generation of anomalous turbulent fluctuations obeying a power law will be discussed in some detail.