Gong Chen Chris, Toenjes Ralf, Pikovsky Arkady
Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Straße 32, 14476 Potsdam, Germany.
Department of Control Theory, Nizhny Novgorod State University, Gagarin Avenue 23, 606950 Nizhny Novgorod, Russia.
Phys Rev E. 2020 Aug;102(2-1):022206. doi: 10.1103/PhysRevE.102.022206.
We propose Möbius maps as a tool to model synchronization phenomena in coupled phase oscillators. Not only does the map provide fast computation of phase synchronization, it also reflects the underlying group structure of the sinusoidally coupled continuous phase dynamics. We study map versions of various known continuous-time collective dynamics, such as the synchronization transition in the Kuramoto-Sakaguchi model of nonidentical oscillators, chimeras in two coupled populations of identical phase oscillators, and Kuramoto-Battogtokh chimeras on a ring, and demonstrate similarities and differences between the iterated map models and their known continuous-time counterparts.
我们提出将莫比乌斯映射作为一种工具，用于对耦合相位振荡器中的同步现象进行建模。该映射不仅能快速计算相位同步，还能反映正弦耦合连续相位动力学的潜在群结构。我们研究了各种已知连续时间集体动力学的映射版本，例如非相同振荡器的Kuramoto-Sakaguchi模型中的同步转变、两个相同相位振荡器耦合群体中的奇异态，以及环上的Kuramoto-Battogtokh奇异态，并展示了迭代映射模型与其已知连续时间对应模型之间的异同。
