论文标题
同步模式的非对称稳定性分析
Symmetry-independent stability analysis of synchronization patterns
论文作者
论文摘要
在引入主稳定函数（MSF）形式主义之后，网络同步领域已经实现了巨大的增长，从而实现了大型振荡器网络中同步的有效稳定性分析。但是，为了取得进一步的进步，我们必须克服这种著名的形式主义的局限性，该形式主义的重点是全球同步，并要求振荡器及其相互作用的功能是相同的，而许多感兴趣的系统本质上是异构的，并且表现出复杂的同步模式。在这里，我们建立了MSF形式主义的概括，即使振荡器和/或它们的相互作用函数是非相同的，也可以表征任何群集同步模式的稳定性。新框架是基于找到变化方程中矩阵的最优质的同时块对角线化，并且不依赖有关网络对称性的信息。这导致了一种比现有的基于对称性的算法更容易容忍的算法，并且比现有的算法快。作为一种应用程序，我们严格地表征了具有多种相互作用类型的网络中嵌合体状态的稳定性。
The field of network synchronization has seen tremendous growth following the introduction of the master stability function (MSF) formalism, which enables the efficient stability analysis of synchronization in large oscillator networks. However, to make further progress we must overcome the limitations of this celebrated formalism, which focuses on global synchronization and requires both the oscillators and their interaction functions to be identical, while many systems of interest are inherently heterogeneous and exhibit complex synchronization patterns. Here, we establish a generalization of the MSF formalism that can characterize the stability of any cluster synchronization pattern, even when the oscillators and/or their interaction functions are nonidentical. The new framework is based on finding the finest simultaneous block diagonalization of matrices in the variational equation and does not rely on information about network symmetry. This leads to an algorithm that is error-tolerant and orders of magnitude faster than existing symmetry-based algorithms. As an application, we rigorously characterize the stability of chimera states in networks with multiple types of interactions.
