Sungkyunkwan University, Department of Physics, Suwon, 16419, Republic of Korea.
Jeonbuk National University, Department of Physics and Research Institute of Physics and Chemistry, Jeonju, 54896, Republic of Korea.
Sci Rep. 2020 Feb 13;10(1):2516. doi: 10.1038/s41598-020-58854-2.
Interacting dynamic agents can often exhibit synchronization. It has been reported that the rhythm all agents agree on in the synchronized state could be different from the average of intrinsic rhythms of individual agents. Hinted by such a real-world behavior of the interaction-driven change of the average phase velocity, we propose a modified version of the Kuramoto model, in which the ith oscillator of the phase ϕ interacts with other oscillator j only when the phase difference [Formula: see text] - [Formula: see text] is in a limited range [-βπ, απ]. From extensive numerical investigations, we conclude that the asymmetric dynamic interaction characterized by β ≠ α leads to the shift of the synchronized frequency with respect to the original distribution of the intrinsic frequency. We also perform and report our computer-based synchronization experiment, which exhibits the expected shift of the synchronized frequency of human participants. In analogy to interacting runners, our result roughly suggests that agents tend to run faster if they are more influenced by runners ahead than behind. We verify the observation by using a simple model of interacting runners.
相互作用的动态主体通常表现出同步性。据报道，在同步状态下所有主体一致的节奏可能与个体主体的固有节奏的平均值不同。这种由相互作用驱动的平均相位速度变化的现实世界行为暗示了我们提出了一种修正的 Kuramoto 模型，其中相位 ϕ 的第 i 个振荡器仅当相位差 [Formula: see text] - [Formula: see text] 在有限的范围[-βπ, απ]内与其他振荡器 j 相互作用。通过广泛的数值研究，我们得出结论，由β ≠ α 表征的不对称动态相互作用导致同步频率相对于固有频率的原始分布发生偏移。我们还进行了并报告了我们的基于计算机的同步实验，该实验表现出人类参与者预期的同步频率的偏移。类似于相互作用的跑步者，我们的结果大致表明，如果跑步者受到前方跑步者的影响大于受到后方跑步者的影响，他们往往会跑得更快。我们通过使用相互作用的跑步者的简单模型验证了这一观察结果。
