@article{9fda73bdf9024a10bdcaf83cbd8824f0,
title = "Intralayer synchronization in evolving multiplex hypernetworks: Analytical approach",
abstract = "In this paper, we study intralayer synchronization of multiplex networks where nodes in each layer interact through diverse types of coupling functions associated with different time-varying network topologies, referred to as multiplex hypernetworks. Here, the intralayer connections are evolving with respect to time, and the interlayer connections are stagnant. In this context, an interesting and important problem is to analyze the stability of the intralayer synchronization in such temporal networks. We prove that if the dynamical multiplex hypernetwork for the time-average topology possesses intralayer synchronization, then each layer of the time-varying multiplex hypernetwork will also be synchronized for sufficiently fast switching. Then through master stability function formalism, we analytically derive necessary and sufficient stability conditions of intralayer synchronous states for such temporal architecture in terms of a time-average network. In this regard, we are able to decouple the transverse error component of the intralayer synchronization states for some special cases. Also, we extend our study for nonlinear intralayer coupling functions as well as multilayer hypernetwork architectures. Finally, the theoretical findings are verified numerically by taking the network of paradigmatic chaotic Rossler oscillators.",
keywords = "Hypernetwork, Master stability function approach, Multilayer network, Synchronization, Time-varying network",
author = "Sarbendu Rakshit and Bera, {Bidesh K.} and Bollt, {Erik M.} and Dibakar Ghosh",
note = "Funding Information: \ast Received by the editors November 2, 2018; accepted for publication (in revised form) by I. Belykh February 5, 2020; published electronically April 23, 2020. https://doi.org/10.1137/18M1224441 Funding: The third author's research was supported by the Army Research Office (USARO) (N68164-EG), the Office of Naval Research (ONR) (N00014-15-1-2093), and the Defense Advanced Research Projects Agency (DARPA). The fourth author's research was supported by SERB-DST (Department of Science and Technology), Government of India (project EMR/2016/001039). \dagger Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, West Bengal, 700108, India (sarbendu.math@gmail.com, diba.ghosh@gmail.com). \ddagger Department of Mathematics, Indian Institute of Technology Ropar, Punjab - 140001, India, and Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, West Bengal, 700108, India (bideshbera18@gmail. com). \S Department of Mathematics, Department of Electrical and Computer Engineering, and Department of Physics, Clarkson University, Potsdam, NY 13699 (ebollt@clarkson.edu). Funding Information: The third author's research was supported by the Army Research Office (USARO) (N68164-EG), the Office of Naval Research (ONR) (N00014-15-1-2093), and the Defense Advanced Research Projects Agency (DARPA). The fourth author's research was supported by SERB-DST (Department of Science and Technology), Government of India (project EMR/2016/001039). Publisher Copyright: {\textcopyright} 2020 Society for Industrial and Applied Mathematics",
year = "2020",
month = jan,
day = "1",
doi = "10.1137/18M1224441",
language = "English",
volume = "19",
pages = "918--963",
journal = "SIAM Journal on Applied Dynamical Systems",
issn = "1536-0040",
publisher = "Society of Industrial and Applied Mathematics",
number = "2",
}