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Chimeras on annuli
1School of Mathematical and Computational Sciences, Massey University, Private Bag 102-904, North Shore Mail Centre, Auckland, New Zealand.
Chaos (Woodbury, N.Y.)
|September 1, 2022
Summary
This study investigates complex chimera states in coupled oscillator networks using a continuum model. Researchers identified conditions for stable chimera solutions and analyzed their bifurcations.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Network science
Background:
- Chimeras, characterized by coexisting synchronous and asynchronous oscillator groups, appear in coupled oscillator networks.
- Understanding chimera dynamics is crucial for various fields, including neuroscience and engineering.
Purpose of the Study:
- To investigate chimera states in networks of nonlocally coupled phase oscillators on an annular domain.
- To analyze the stability and bifurcations of chimera solutions and rotating waves.
Main Methods:
- Utilized the Ott/Antonsen ansatz for a continuum-level description of oscillator dynamics.
- Employed numerical analysis of the order parameter equations.
- Investigated solutions analogous to multi-headed and spiral wave chimeras.
Main Results:
- Identified stable chimera solutions on annular domains, dependent on domain width.
- Characterized rotating waves with different winding numbers, analogous to spiral wave chimeras.
- Determined parameter ranges for the existence and stability of these solutions, noting subcritical bifurcations.
Conclusions:
- Chimera states exhibit complex behaviors in annular domains, with stability contingent on domain size.
- The study provides insights into the formation and stability of chimera patterns in extended systems.
- Subcritical bifurcations govern the loss of stability for observed chimera and rotating wave solutions.
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