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Frequency assortativity can induce chaos in oscillator networks
Per Sebastian Skardal1,2, Juan G Restrepo3, Edward Ott4
1Department of Mathematics, Trinity College, Hartford, Connecticut 06106, USA.
Summary
Frequency assortativity in coupled oscillator networks can lead to macroscopic chaos. This chaos arises from the formation of synchronized oscillator groups, known as meta-oscillators.
Area of Science:
- Complex systems
- Network science
- Nonlinear dynamics
Background:
- Coupled phase oscillators are fundamental in modeling diverse phenomena.
- Network structure significantly influences system dynamics.
- Frequency assortativity, preferential linking of similar frequencies, is a key network property.
Purpose of the Study:
- To investigate the impact of frequency assortativity on the macroscopic dynamics of coupled oscillator networks.
- To understand the mechanisms driving chaotic behavior in such networks.
- To characterize macroscopic chaos using analytical and computational methods.
Main Methods:
- Utilized the network Kuramoto model as a representative system.
- Applied mean-field approximation and Ott-Antonsen dimension reduction.
- Analyzed macroscopic chaos via Lyapunov exponents, bifurcation diagrams, and time-delay embeddings.
Main Results:
- Frequency assortativity was found to induce chaos in macroscopic dynamics.
- The complex dynamics were successfully reduced to a low-dimensional system.
- Chaos was linked to the emergence of synchronized oscillator groups (meta-oscillators).
Conclusions:
- Frequency assortativity is a critical factor in generating macroscopic chaos in oscillator networks.
- The formation of meta-oscillators provides a mechanism for understanding emergent chaotic behavior.
- The study offers insights into the complex dynamics of structured oscillatory systems.
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