Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom and Wellcome Trust/Cancer Research UK Gurdon Institute, University of Cambridge, Tennis Court Road, Cambridge CB2 1QN, United Kingdom.
Phys Rev E. 2017 Sep;96(3-1):032201. doi: 10.1103/PhysRevE.96.032201. Epub 2017 Sep 1.
We present a generalization of the Kuramoto phase oscillator model in which phases advance in discrete phase increments through Poisson processes, rendering both intrinsic oscillations and coupling inherently stochastic. We study the effects of phase discretization on the synchronization and precision properties of the coupled system both analytically and numerically. Remarkably, many key observables such as the steady-state synchrony and the quality of oscillations show distinct extrema while converging to the classical Kuramoto model in the limit of a continuous phase. The phase-discretized model provides a general framework for coupled oscillations in a Markov chain setting.
我们提出了一种推广的 Kuramoto 相位振荡器模型，其中相位通过泊松过程以离散的相位增量前进，从而使固有振荡和耦合都具有随机性。我们通过理论分析和数值模拟研究了相位离散化对耦合系统的同步和精度特性的影响。值得注意的是，许多关键的观测量，如稳态同步和振荡质量，在连续相位极限下收敛到经典 Kuramoto 模型时，表现出明显的极值。离散相位模型为马尔可夫链环境中的耦合振荡提供了一个通用框架。
