Hong Hyunsuk
Department of Physics and Research Institute of Physics and Chemistry, Chonbuk National University, Jeonju 561-756, South Korea.
Chaos. 2018 Oct;28(10):103112. doi: 10.1063/1.5039564.
We consider a system of coupled swarmalators moving in two dimensional space and explore its collective behavior. Here the swarmalators represent the oscillators that can sync and swarm in space, following the previous study [O'Keeffe , Nat. Commun., , 1504 (2017)]. The internal state of each swarmalator is represented by its phase angle, and the swarmalators are free to move in the plane according to an equation of motion where the phase and spatial dynamics are coupled with each other. In particular, the phase coupling between the swarmalators is attractive (positive) one, so the coupling makes the swarmalators have their phase difference minimized. The collective behavior of the system is found to be different depending on the extent of the interplay between the phase and spatial dynamics: Specifically, when the extent of the interplay between the phase and spatial dynamics is so weak as to be negligible, the phase dynamics of our system recovers that of the conventional mean-field model. On the other hand, when a certain extent of the interplay is present, the system is found to exhibit the phase where the overall order does not occur. Interestingly, it is found that the correlated phase is the same as the active phase wave found in the system of swarmalators with repulsive phase coupling [O'Keeffe , Nat. Commun., , 1504 (2017)]. We also find that the system exhibits two different phase transitions: One is the transition from the sync state to the active phase wave state, and the other one is the transition from the active phase wave state to the async state. We perform the finite-size scaling analysis and investigate the transition nature.
我们考虑一个在二维空间中运动的耦合群振子系统，并探究其集体行为。这里的群振子代表能够在空间中同步和聚集的振子，这是基于之前的研究[奥基夫，《自然·通讯》，，1504（2017）]。每个群振子的内部状态由其相位角表示，并且群振子可以根据一个运动方程在平面内自由移动，其中相位和空间动力学相互耦合。特别地，群振子之间的相位耦合是吸引性的（正的），所以这种耦合使得群振子的相位差最小化。发现该系统的集体行为会根据相位和空间动力学之间相互作用的程度而有所不同：具体来说，当相位和空间动力学之间的相互作用程度弱到可以忽略不计时，我们系统的相位动力学恢复为传统平均场模型的相位动力学。另一方面，当存在一定程度的相互作用时，发现该系统会呈现出整体秩序不出现的相位。有趣的是，发现相关相位与在具有排斥性相位耦合的群振子系统中发现的活性相位波相同[奥基夫，《自然·通讯》，，1504（2017）]。我们还发现该系统呈现出两种不同的相变：一种是从同步状态到活性相位波状态的转变，另一种是从活性相位波状态到异步状态的转变。我们进行有限尺寸标度分析并研究转变性质。
