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Partial synchronization in networks of non-linearly coupled oscillators: The Deserter Hubs Model
- We study the Deserter Hubs Model: a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity of interactions. Under weak force, an oscillator tends to follow the phase of its neighbors, but if an oscillator is compelled to follow its peers by a sufficient large number of cohesive neighbors, then it actually starts to act in the opposite manner, i.e., in anti-phase with the majority. Analytic results yield that if the repulsion parameter is small enough in comparison with the degree of the maximum hub, then the full synchronization state is locally stable. Numerical experiments are performed to explore the model beyond this threshold, where the overall cohesion is lost. We report in detail partially synchronous dynamical regimes, like stationary phase-locking, multistability, periodic and chaotic states. Via statistical analysis of different network organizations like tree, scale-free, and random ones, we found a measure allowing oneWe study the Deserter Hubs Model: a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity of interactions. Under weak force, an oscillator tends to follow the phase of its neighbors, but if an oscillator is compelled to follow its peers by a sufficient large number of cohesive neighbors, then it actually starts to act in the opposite manner, i.e., in anti-phase with the majority. Analytic results yield that if the repulsion parameter is small enough in comparison with the degree of the maximum hub, then the full synchronization state is locally stable. Numerical experiments are performed to explore the model beyond this threshold, where the overall cohesion is lost. We report in detail partially synchronous dynamical regimes, like stationary phase-locking, multistability, periodic and chaotic states. Via statistical analysis of different network organizations like tree, scale-free, and random ones, we found a measure allowing one to predict relative abundance of partially synchronous stationary states in comparison to time-dependent ones. (C) 2015 AIP Publishing LLC.…
Author details: | Celso Freitas, Elbert Macau, Arkadij PikovskijORCiDGND |
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DOI: | https://doi.org/10.1063/1.4919246 |
ISSN: | 1054-1500 |
ISSN: | 1089-7682 |
Pubmed ID: | https://pubmed.ncbi.nlm.nih.gov/25933667 |
Title of parent work (English): | Chaos : an interdisciplinary journal of nonlinear science |
Publisher: | American Institute of Physics |
Place of publishing: | Melville |
Publication type: | Article |
Language: | English |
Year of first publication: | 2015 |
Publication year: | 2015 |
Release date: | 2017/03/27 |
Volume: | 25 |
Issue: | 4 |
Number of pages: | 8 |
Funding institution: | Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior-CAPES [Process: BEX 10571/13-2]; DFG/FAPESP [IRTG 1740/TRP 2011/50151-0]; CNPq; Russian Ministry of Education and Science [02.B.49.21.0003]; Lobachevsky State University of Nizhni Novgorod [02.B.49.21.0003] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
Peer review: | Referiert |