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Complex localization mechanisms in networks of coupled oscillators: Two case studies
Zachary G Nicolaou1, Jason J Bramburger2
1Department of Applied Mathematics, University of Washington, Seattle, Washington 98195-3925, USA.
Chaos (Woodbury, N.Y.)
|January 22, 2024
Summary
This study explores localized dynamical phenomena in coupled oscillator systems, revealing novel bifurcation routes and complex behaviors like chaotic tangles. It highlights the role of symmetries in these localized states.
Area of Science:
- Nonlinear Dynamics
- Complex Systems
- Theoretical Physics
Background:
- Localized phenomena are prevalent across physical sciences.
- Previous research focused on steady states, but dynamical localization in coupled oscillators is a recent area of interest.
- Known examples include chimera patterns and gap solitons in driven oscillator networks.
Purpose of the Study:
- To numerically investigate localized time-periodic states in coupled oscillator systems.
- To document the various bifurcations these states undergo.
- To identify new mechanisms leading to localization.
Main Methods:
- Numerical continuation techniques were employed.
- Analysis of bifurcations of localized states.
- Investigation of systems including Janus oscillators and parametrically driven pendula arrays.
Main Results:
- Novel routes to localization were discovered, involving heteroclinic cycle bifurcations.
- Complex bifurcation diagrams, resembling chaotic tangles, were observed.
- The significant influence of discrete symmetries and symmetric branch points was demonstrated.
Conclusions:
- Symmetries play a crucial role in the emergence and behavior of localized states in coupled oscillators.
- Complex dynamics, including chaos, can arise from bifurcations of localized states.
- This work expands the understanding of dynamical localization in physical systems.
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