论文标题
独眼巨人在排斥库拉莫托网络中的状态：高阶耦合的作用
Cyclops states in repulsive Kuramoto networks: the role of higher-order coupling
论文作者
论文摘要
排斥振荡器网络可以表现出多种合作节奏，包括嵌合体和簇状状态。然而，了解哪些节奏占上风仍然具有挑战性。在这里，我们在具有高阶耦合的相同旋转器的Kuramoto-Sakaguchi网络的背景下解决了这个基本问题。通过分析和数字，我们表明，具有两个不同相干簇和一个孤立振荡器的三个群集pl态是具有奇数单位的网络中的普遍节奏。我们用独立振荡器让人联想到独眼巨人的眼睛，表示独立的三脚架模式。作为神话对应物，独眼巨人的状态是巨人，在弱势网络中以一阶耦合占据了系统的相位空间。令人惊讶的是，在库拉莫托耦合功能中增加了第二或第三个谐波，使独眼巨人几乎在整个耦合的排斥范围内都表明了全球吸引子。在更一般的层面上，我们的结果提出了在排斥物理和生物网络中寻找主导节奏的线索。
Repulsive oscillator networks can exhibit multiple cooperative rhythms, including chimera and cluster splay states. Yet, understanding which rhythm prevails remains challenging. Here, we address this fundamental question in the context of Kuramoto-Sakaguchi networks of identical rotators with higher-order coupling. Through analysis and numerics, we show that three-cluster splay states with two distinct coherent clusters and a solitary oscillator are the prevalent rhythms in networks with an odd number of units. We denote such tripod patterns cyclops states with the solitary oscillator reminiscent of the Cyclops's eye. As their mythological counterparts, the cyclops states are giants that dominate the system's phase space in weakly repulsive networks with first-order coupling. Astonishingly, the addition of the second or third harmonics to the Kuramoto coupling function makes the cyclops states global attractors practically across the full range of coupling's repulsion. At a more general level, our results suggest clues for finding dominant rhythms in repulsive physical and biological networks.
