Localized phenomena abound in nature and throughout the physical sciences. Some universal mechanisms for localization have been characterized, such as in the snaking bifurcations of localized steady states in pattern-forming partial differential equations. While much of this understanding has been targeted at steady states, recent studies have noted complex dynamical localization phenomena in systems of coupled oscillators. These localized states can come in the form of symmetry-breaking chimera patterns that exhibit coexistence of coherence and incoherence in symmetric networks of coupled oscillators and gap solitons emerging in the bandgap of parametrically driven networks of oscillators. Here, we report detailed numerical continuations of localized time-periodic states in systems of coupled oscillators, while also documenting the numerous bifurcations they give way to. We find novel routes to localization involving bifurcations of heteroclinic cycles in networks of Janus oscillators and strange bifurcation diagrams resembling chaotic tangles in a parametrically driven array of coupled pendula. We highlight the important role of discrete symmetries and the symmetric branch points that emerge in symmetric models.
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January 2024
Research Article|
January 22 2024
Complex localization mechanisms in networks of coupled oscillators: Two case studies
Special Collection:
Regime switching in coupled nonlinear systems: sources, prediction, and control
Zachary G. Nicolaou
;
Zachary G. Nicolaou
a)
(Conceptualization, Formal analysis, Writing – original draft, Writing – review & editing)
1
Department of Applied Mathematics, University of Washington
, Seattle, Washington 98195-3925, USA
a)Author to whom correspondence should be addressed: [email protected]
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Jason J. Bramburger
Jason J. Bramburger
(Conceptualization, Formal analysis, Writing – original draft, Writing – review & editing)
2
Department of Mathematics and Statistics, Concordia University
, Montréal, Quebec H3G 1M8, Canada
Search for other works by this author on:
a)Author to whom correspondence should be addressed: [email protected]
Chaos 34, 013131 (2024)
Article history
Received:
August 31 2023
Accepted:
December 14 2023
Citation
Zachary G. Nicolaou, Jason J. Bramburger; Complex localization mechanisms in networks of coupled oscillators: Two case studies. Chaos 1 January 2024; 34 (1): 013131. https://doi.org/10.1063/5.0174550
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