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Phase synchronization and topological defects in inhomogeneous media
Jörn Davidsen1, Raymond Kapral
1Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Canada ON M5S 3H6. joern.davidsen@utoronto.ca
Summary
Topological defects disrupt phase synchronization in chaotic oscillator arrays. Stronger coupling prevents defect creation, maintaining phase coherence and suggesting modified synchronization concepts for higher dimensions.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Chaos theory
Background:
- Phase synchronization is crucial in coupled oscillator systems.
- Topological defects can emerge in 2D and higher-dimensional systems.
- Nonidentical chaotic oscillators present unique synchronization challenges.
Purpose of the Study:
- Investigate the impact of topological defects on phase synchronization.
- Analyze phase coherence in 2D arrays of nonidentical chaotic oscillators.
- Determine the role of coupling strength in defect dynamics and synchronization.
Main Methods:
- Simulations of locally coupled, nonidentical, chaotic oscillators in 2D arrays.
- Analysis of defect motion and its effect on phase synchronization.
- Varying coupling strengths to observe changes in defect dynamics and coherence.
Main Results:
- Topological defect motion causes localized breakdown of phase synchronization.
- Sufficiently strong coupling inhibits continuous defect creation/annihilation, preserving phase coherence.
- The presence of defects fundamentally challenges standard phase synchronization definitions.
Conclusions:
- Topological defects are significant factors influencing phase synchronization in chaotic oscillator networks.
- Phase coherence can be maintained if coupling strength prevents defect proliferation.
- The concept of phase synchronization requires re-evaluation for systems exhibiting topological defects.