Master stability functions for complete, intralayer, and interlayer synchronization in multiplex networks of coupled Rössler oscillators

Longkun Tang, Xiaoqun Wu, Jinhu Lü, Jun-an Lu, and Raissa M. D'Souza
Phys. Rev. E 99, 012304 – Published 3 January 2019

Abstract

Synchronization phenomena are of broad interest across disciplines and increasingly of interest in a multiplex network setting. For the multiplex network of coupled Rössler oscillators, here we show how the master stability function, a celebrated framework for analyzing synchronization on a single network, can be extended to certain classes of multiplex networks with different intralayer and interlayer coupling functions. We derive three master stability equations that determine, respectively, the necessary regions of complete synchronization, intralayer synchronization, and interlayer synchronization. We calculate these three regions explicitly for the case of a two-layer network of Rössler oscillators and show that the overlap of the regions determines the type of synchronization achieved. In particular, if the interlayer or intralayer coupling function is such that the interlayer or intralayer synchronization region is empty, complete synchronization cannot be achieved regardless of the coupling strength. Furthermore, for any network structure, the occurrence of intralayer and interlayer synchronization depends mainly on the coupling functions of nodes within a layer and across layers, respectively. Our mathematical analysis requires that the intralayer and interlayer supra-Laplacians commute. But, we show this is only a sufficient, and not necessary, condition and that the results can be applied more generally.

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  • Received 10 December 2017

DOI:https://doi.org/10.1103/PhysRevE.99.012304

©2019 American Physical Society

Physics Subject Headings (PhySH)

NetworksNonlinear Dynamics

Authors & Affiliations

Longkun Tang1, Xiaoqun Wu2,3,*, Jinhu Lü4, Jun-an Lu2, and Raissa M. D'Souza3

  • 1Fujian Province University Key Laboratory of Computation Science, School of Mathematical Science, Huaqiao University, Quanzhou 362021, China
  • 2School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • 3Department of Computer Science, University of California, Davis, California 95616, USA
  • 4School of Automation Science and Electrical Engineering, State Key Laboratory of Software Development Environment, and Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing 100191, China

  • *To whom correspondence should be addressed: xqwu@whu.edu.cn

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Vol. 99, Iss. 1 — January 2019

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