Synchronization patterns and stability of solutions in multiplex networks of nonlinear oscillators

Networks with different levels of interactions, including multilayer and multiplex networks, can display a rich diversity of dynamical behaviors and can be used to model and study a wide range of systems. Despite numerous efforts to investigate these networks, obtaining mathematical descriptions for the dynamics of multilayer and multiplex systems is still an open problem. Here, we combine ideas and concepts from linear algebra and graph theory with nonlinear dynamics to offer a novel approach to study multiplex networks of Kuramoto oscillators. Our approach allows us to study the dynamics of a large, multiplex network by decomposing it into two smaller systems: one representing the connection scheme within layers, and the other representing the connections between layers. With this, we can study synchronization patterns and the linear stability of the solutions that emerge in multiplex networks of nonlinear oscillators.

[1]  M. Perc,et al.  Signal propagation in complex networks , 2023, Physics Reports.

[2]  Roberto C. Budzinski,et al.  Broadcasting solutions on networked systems of phase oscillators , 2022, Chaos, Solitons & Fractals.

[3]  Gabriel B. Benigno,et al.  Analytical prediction of specific spatiotemporal patterns in nonlinear oscillator networks with distance-dependent time delays , 2022, Physical Review Research.

[4]  L. Muller,et al.  Joins of circulant matrices , 2021, Linear Algebra and its Applications.

[5]  Roberto C. Budzinski,et al.  Equilibria in Kuramoto Oscillator Networks: An Algebraic Approach , 2021, SIAM J. Appl. Dyn. Syst..

[6]  Roberto C. Budzinski,et al.  Geometry unites synchrony, chimeras, and waves in nonlinear oscillator networks , 2021, Chaos.

[7]  Matjaz Perc,et al.  Social physics , 2021, Physics Reports.

[8]  E. Rybalova,et al.  Interplay between solitary states and chimeras in multiplex neural networks , 2021, Chaos, Solitons & Fractals.

[9]  H. Poor,et al.  Topological clustering of multilayer networks , 2021, Proceedings of the National Academy of Sciences.

[10]  U. Feudel,et al.  Asymmetry-induced order in multilayer networks. , 2021, Physical review. E.

[11]  S. Jalan,et al.  Explosive synchronization in interlayer phase-shifted Kuramoto oscillators on multiplex networks. , 2021, Chaos.

[12]  V. Mehrmann,et al.  The Multiplex Decomposition: An Analytic Framework for Multilayer Dynamical Networks , 2021, SIAM J. Appl. Dyn. Syst..

[13]  Leonhard Schuelen,et al.  Solitary states in multiplex neural networks: Onset and vulnerability , 2020, 2009.11639.

[14]  S. R. Lopes,et al.  Ecology and signal structure drive the evolution of synchronous displays * , 2020, Evolution; international journal of organic evolution.

[15]  Sarika Jalan,et al.  Interlayer adaptation-induced explosive synchronization in multiplex networks , 2019, 1910.10433.

[16]  Anil Kumar,et al.  Explosive synchronization in frequency displaced multiplex networks. , 2019, Chaos.

[17]  Sarika Jalan,et al.  Inhibition-induced explosive synchronization in multiplex networks. , 2019, Physical review. E.

[18]  Chittaranjan Hens,et al.  Explosive synchronization in phase-frustrated multiplex networks , 2018, Physical Review E.

[19]  Jürgen Kurths,et al.  Macroscopic chimeralike behavior in a multiplex network. , 2018, Physical review. E.

[20]  Iryna Omelchenko,et al.  Delay controls chimera relay synchronization in multiplex networks , 2018, Physical Review E.

[21]  J. Gold,et al.  On the nature and use of models in network neuroscience , 2018, Nature Reviews Neuroscience.

[22]  Yamir Moreno,et al.  Multilayer Networks in a Nutshell , 2018, Annual Review of Condensed Matter Physics.

[23]  Terrence J. Sejnowski,et al.  Cortical travelling waves: mechanisms and computational principles , 2018, Nature Reviews Neuroscience.

[24]  Olaf Sporns,et al.  Communication dynamics in complex brain networks , 2017, Nature Reviews Neuroscience.

[25]  R Sevilla-Escoboza,et al.  Relay synchronization in multiplex networks , 2017, Scientific Reports.

[26]  M. Perc,et al.  Network science of biological systems at different scales: A review. , 2017, Physics of life reviews.

[27]  Marc Timme,et al.  Dynamically induced cascading failures in power grids , 2017, Nature Communications.

[28]  Fred Wolf,et al.  Flexible information routing by transient synchrony , 2017, Nature Neuroscience.

[29]  O. Sporns,et al.  Network neuroscience , 2017, Nature Neuroscience.

[30]  R. Sevilla-Escoboza,et al.  Inter-layer synchronization in non-identical multi-layer networks , 2016, Scientific Reports.

[31]  Sarika Jalan,et al.  Birth and death of chimera: Interplay of delay and multiplexing , 2016, 1610.01761.

[32]  M. A. Porter,et al.  The physics of spreading processes in multilayer networks , 2016, Nature Physics.

[33]  E. Schöll,et al.  Chimera patterns induced by distance-dependent power-law coupling in ecological networks. , 2016, Physical review. E.

[34]  Thomas K. D. M. Peron,et al.  The Kuramoto model in complex networks , 2015, 1511.07139.

[35]  Jurgen Kurths,et al.  Synchronization in delayed multiplex networks , 2015, 1605.00352.

[36]  Sarika Jalan,et al.  Emergence of Chimera in Multiplex Network , 2015, Int. J. Bifurc. Chaos.

[37]  Louis M Pecora,et al.  Synchronization of chaotic systems. , 2015, Chaos.

[38]  Ginestra Bianconi,et al.  Control of Multilayer Networks , 2015, Scientific Reports.

[39]  Nikos E. Kouvaris,et al.  Pattern formation in multiplex networks , 2014, Scientific Reports.

[40]  Zonghua Liu,et al.  Explosive synchronization in adaptive and multilayer networks. , 2014, Physical review letters.

[41]  Mattia Frasca,et al.  Intra-layer synchronization in multiplex networks , 2014, 1407.3283.

[42]  Z. Wang,et al.  The structure and dynamics of multilayer networks , 2014, Physics Reports.

[43]  Vito Latora,et al.  Collective Phenomena Emerging from the Interactions between Dynamical Processes in Multiplex Networks. , 2014, Physical review letters.

[44]  Matteo Magnani,et al.  Spreading Processes in Multilayer Networks , 2014, IEEE Transactions on Network Science and Engineering.

[45]  Vito Latora,et al.  Measuring and modelling correlations in multiplex networks , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[46]  Mason A. Porter,et al.  Multilayer networks , 2013, J. Complex Networks.

[47]  Vito Latora,et al.  Structural measures for multiplex networks. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[48]  A. Arenas,et al.  Mathematical Formulation of Multilayer Networks , 2013, 1307.4977.

[49]  Seth A. Myers,et al.  Spontaneous synchrony in power-grid networks , 2013, Nature Physics.

[50]  Luis Mario Floría,et al.  Evolution of Cooperation in Multiplex Networks , 2012, Scientific Reports.

[51]  Conrado J. Pérez Vicente,et al.  Diffusion dynamics on multiplex networks , 2012, Physical review letters.

[52]  H. Stanley,et al.  Networks formed from interdependent networks , 2011, Nature Physics.

[53]  O. Sporns,et al.  Key role of coupling, delay, and noise in resting brain fluctuations , 2009, Proceedings of the National Academy of Sciences.

[54]  Daniel J. Brass,et al.  Network Analysis in the Social Sciences , 2009, Science.

[55]  Jurgen Kurths,et al.  Synchronization in complex networks , 2008, 0805.2976.

[56]  R. Spigler,et al.  The Kuramoto model: A simple paradigm for synchronization phenomena , 2005 .

[57]  S. Strogatz.  From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators , 2000 .

[58]  Sarah Rothstein,et al.  An Introduction To The Theory Of Graph Spectra , 2016 .