广义多层高阶网络中的全局同步性

Palash Kumar Pal, Md Sayeed Anwar, Matjaz Perc, Dibakar Ghosh
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引用次数: 0

摘要

人们越来越认识到,包含高阶相互作用的网络能够在各种过程中引入新的动态,包括同步。以往对多层网络同步性的研究往往局限于特定模型,如 Kuramoto 模型,或者只关注单个层内的高阶相互作用。在这里,我们提出了一个综合框架,用于研究具有高阶交互作用的多层网络中的同步性,尤其是全局同步性。我们的框架考虑了层内和层间成对连接之外的相互作用。我们证明了稳定的全局同步状态的存在,其条件类似于主稳定函数,取决于耦合函数的选择。我们的理论发现得到了使用 Hindmarsh-Rose 神经元和 R\"{o}ssleroscillators 进行的模拟的支持。这些模拟说明了层内和层间的高阶相互作用是如何促进同步的,突出了与涉及单层内相互作用的情景相比的优势。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Global synchronization in generalized multilayer higher-order networks
Networks incorporating higher-order interactions are increasingly recognized for their ability to introduce novel dynamics into various processes, including synchronization. Previous studies on synchronization within multilayer networks have often been limited to specific models, such as the Kuramoto model, or have focused solely on higher-order interactions within individual layers. Here, we present a comprehensive framework for investigating synchronization, particularly global synchronization, in multilayer networks with higher-order interactions. Our framework considers interactions beyond pairwise connections, both within and across layers. We demonstrate the existence of a stable global synchronous state, with a condition resembling the master stability function, contingent on the choice of coupling functions. Our theoretical findings are supported by simulations using Hindmarsh-Rose neuronal and R\"{o}ssler oscillators. These simulations illustrate how synchronization is facilitated by higher-order interactions, both within and across layers, highlighting the advantages over scenarios involving interactions within single layers.
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