论文标题
具有非局部高阶相互作用的相位振荡器网络：扭曲状态，稳定性和分叉
Phase Oscillator Networks with Nonlocal Higher-Order Interactions: Twisted States, Stability and Bifurcations
论文作者
论文摘要
Kuramoto模型为相互作用的粒子系统中的同步现象提供了一个原型框架。除了全相同步外，所有振荡器的行为表现相同，具有环状非局部耦合的库拉莫托振荡器还可以表现出更复杂的模式，例如均匀扭曲的状态。 Wiley，Strogatz和Girvan在2006年发现了这些扭曲状态的稳定性取决于每个振荡器的耦合范围。在本文中，我们分析了扭曲的状态及其分叉在环形非本地耦合的无限粒子极限中。我们不仅像库拉马托模型一样考虑传统的成对相互作用，而且还展示了高阶非脚部相互作用的影响，这是自然而然地在相减少中产生的。我们阐明了成对和非层的相互作用如何影响扭曲状态的稳定性，计算分叉分支，并表明高阶相互作用可以稳定如果耦合仅成对，这些扭曲状态是不稳定的。
The Kuramoto model provides a prototypical framework to synchronization phenomena in interacting particle systems. Apart from full phase synchrony where all oscillators behave identically, identical Kuramoto oscillators with ring-like nonlocal coupling can exhibit more elaborate patterns such as uniformly twisted states. It was discovered by Wiley, Strogatz and Girvan in 2006 that the stability of these twisted states depends on the coupling range of each oscillator. In this paper, we analyze twisted states and their bifurcations in the infinite particle limit of ring-like nonlocal coupling. We not only consider traditional pairwise interactions as in the Kuramoto model but also demonstrate the effects of higher-order nonpairwise interactions, which arise naturally in phase reductions. We elucidate how pairwise and nonpairwise interactions affect the stability of the twisted states, compute bifurcating branches, and show that higher-order interactions can stabilize twisted states that are unstable if the coupling is only pairwise.
