School of Life Sciences, University of Warwick, Coventry CV4 7AL, U.K.
Departamento de Física de la Materia Condensada, University of Zaragoza, 50009 Zaragoza, Spain.; Institute for Biocomputation and Physics of Complex Systems, University of Zaragoza, 50018 Zaragoza, Spain.
Sci Adv. 2016 Nov 16;2(11):e1601679. doi: 10.1126/sciadv.1601679. eCollection 2016 Nov.
The structure of many real-world systems is best captured by networks consisting of several interaction layers. Understanding how a multilayered structure of connections affects the synchronization properties of dynamical systems evolving on top of it is a highly relevant endeavor in mathematics and physics and has potential applications in several socially relevant topics, such as power grid engineering and neural dynamics. We propose a general framework to assess the stability of the synchronized state in networks with multiple interaction layers, deriving a necessary condition that generalizes the master stability function approach. We validate our method by applying it to a network of Rössler oscillators with a double layer of interactions and show that highly rich phenomenology emerges from this. This includes cases where the stability of synchronization can be induced even if both layers would have individually induced unstable synchrony, an effect genuinely arising from the true multilayer structure of the interactions among the units in the network.
许多现实世界系统的结构最好用由几个交互层组成的网络来描述。理解连接的多层结构如何影响在其之上演变的动力系统的同步特性，是数学和物理学中一个非常相关的研究领域，并且在几个与社会相关的主题中具有潜在的应用，例如电网工程和神经动力学。我们提出了一个通用框架来评估具有多个交互层的网络中同步状态的稳定性，推导出一个必要条件，该条件推广了主稳定性函数方法。我们通过将其应用于具有双层相互作用的罗瑟勒振荡器网络来验证我们的方法，并表明从中出现了非常丰富的现象。这包括即使两个层各自都会引起不稳定的同步，同步稳定性也可以被诱导的情况，这种情况确实是由于网络中单元之间的真实多层相互作用结构而产生的。
