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Nonstationary coherence-incoherence patterns in nonlocally coupled heterogeneous phase oscillators
1Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam, Germany.
Chaos (Woodbury, N.Y.)
|May 3, 2020
Summary
This study reveals nonstationary coherence-incoherence patterns (CIPs) in coupled phase oscillators. Introducing heterogeneity stabilizes these dynamic states, expanding their parameter range and revealing complex behaviors.
Area of Science:
- Nonlinear dynamics
- Complex systems
- Statistical physics
Background:
- Chimera states represent a fascinating phenomenon in coupled oscillator systems, exhibiting coexisting regions of coherence and incoherence.
- Previous research primarily focused on stationary chimera states, with limited exploration of their dynamic counterparts.
Purpose of the Study:
- To investigate the existence and properties of nonstationary coherence-incoherence patterns (CIPs) in large rings of nonlocally coupled phase oscillators.
- To explore the influence of system heterogeneity on the stability and characteristics of these nonstationary patterns.
- To analyze the underlying bifurcation mechanisms governing the transitions between different types of nonstationary CIPs.
Main Methods:
- Theoretical analysis using a mean-field equation for the infinite system limit.
- Direct numerical simulations of both the mean-field equation and the original coupled oscillator system.
- Investigation of parameter spaces to identify stability regions and bifurcation scenarios.
Main Results:
- Identified nonstationary coherence-incoherence patterns (CIPs) in addition to stationary chimera states.
- Demonstrated that introducing spatially uniform heterogeneity significantly enlarges the stability region of nonstationary CIPs.
- Observed different types of nonstationary CIPs, including pulsing and alternating behaviors, through numerical simulations.
- Revealed a complex bifurcation scenario governing the transformations between these dynamic states.
Conclusions:
- Nonstationary CIPs are a robust feature of nonlocally coupled phase oscillators, particularly when system heterogeneity is present.
- Heterogeneity plays a crucial role in stabilizing and expanding the parameter space for dynamic coherence-incoherence phenomena.
- The study provides a comprehensive understanding of the complex dynamics and bifurcations associated with nonstationary chimera-like states.
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