Gilg Brady, Armbruster Dieter
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85257-1804, USA.
Chaos. 2019 May;29(5):053122. doi: 10.1063/1.5084063.
The Kuramoto model is an archetypal model for studying synchronization in groups of nonidentical oscillators. Each oscillator is imbued with its own personal inherent driving frequency and experiences attractive coupling forces toward all the other oscillators in the system. As the coupling increases, there exists a minimal coupling strength called the critical coupling beyond which the system moves in a collective rhythm. A unified approach for creating approximations of the critical coupling is created. It is based on an interpretation of a measurement of phase synchronization among the oscillators (the order parameter) as a function of the coupling strength. The approach allows a graphical way to develop new approximations that are provably, strict lower bounds. It is shown that several of the critical coupling bounds that have been previously studied can be interpreted in this unified framework. In addition, a process based on fixed point sampling is introduced that converts upper bounds for the critical coupling into associated lower bounds.
仓本模型是用于研究非相同振子群体同步性的典型模型。每个振子都有其自身固有的驱动频率，并受到系统中所有其他振子的吸引耦合作用。随着耦合增强，存在一个称为临界耦合的最小耦合强度，超过该强度后系统将以集体节奏运动。创建了一种用于生成临界耦合近似值的统一方法。它基于将振子间相位同步的测量值（序参量）解释为耦合强度的函数。该方法提供了一种图形化方式来开发新的近似值，这些近似值可被证明是严格的下界。结果表明，先前研究的几个临界耦合界限可以在这个统一框架中得到解释。此外还引入了一种基于定点采样的过程，该过程将临界耦合的上界转换为相关的下界。
