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Topological synchronization of coupled nonlinear oscillators
- Publication Year :
- 2020
- Publisher :
- arXiv, 2020.
-
Abstract
- Synchronization of coupled oscillators is a ubiquitous phenomenon found throughout nature. Its robust realization is crucial to our understanding of various nonlinear systems, ranging from biological functions to electrical engineering. On another front, in condensed matter physics, topology is utilized to realize robust properties like topological edge modes, as demonstrated by celebrated topological insulators. Here, we integrate these two research avenues and propose a nonlinear topological phenomenon, namely topological synchronization, where only the edge oscillators synchronize while the bulk ones exhibit chaotic dynamics. We analyze concrete prototypical models to demonstrate the presence of positive Lyapunov exponents and Lyapunov vectors localized along the edge. As a unique characteristic of topology in nonlinear systems, we find that unconventional extra topological boundary modes appear at emerging effective boundaries. Furthermore, our proposal shows promise for spatially controlling synchronization, such as on-demand pattern designing and defect detection. The topological synchronization can ubiquitously appear in topological nonlinear oscillators and thus can provide a guiding principle to realize synchronization in a robust, geometrical, and flexible way.<br />Comment: 24 pages, 26 figures
- Subjects :
- Condensed Matter - Other Condensed Matter
Condensed Matter - Mesoscale and Nanoscale Physics
Statistical Mechanics (cond-mat.stat-mech)
Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
General Physics and Astronomy
FOS: Physical sciences
Chaotic Dynamics (nlin.CD)
Nonlinear Sciences - Chaotic Dynamics
Adaptation and Self-Organizing Systems (nlin.AO)
Nonlinear Sciences - Adaptation and Self-Organizing Systems
Condensed Matter - Statistical Mechanics
Other Condensed Matter (cond-mat.other)
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....ccf2af979c6550398dd4759dc14bc17a
- Full Text :
- https://doi.org/10.48550/arxiv.2012.09479