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Spectral properties of chimera states
M Wolfrum1, O E Omel'chenko, S Yanchuk
1Weierstrass Institute, Mohrenstr. 39, 10117 Berlin, Germany.
Chaos (Woodbury, N.Y.)
|April 5, 2011
Summary
Chimera states exhibit hyperchaotic dynamics in finite systems. In the thermodynamic limit, these states become neutrally stable, with spectral properties matching finite system limits.
Area of Science:
- Nonlinear dynamics
- Complex systems
- Statistical physics
Background:
- Chimera states are spatiotemporal patterns in coupled oscillator systems, characterized by coexisting coherent and incoherent dynamics.
- Understanding the spectral properties of chimera states is crucial for characterizing their stability and dynamics.
Purpose of the Study:
- To analyze the spectral properties of chimera states in phase oscillator systems.
- To investigate the relationship between Lyapunov spectra, system size, and the number of incoherent oscillators.
- To analytically determine the spectral properties in the thermodynamic limit.
Main Methods:
- Numerical computation of Lyapunov spectra for systems with an increasing number of oscillators.
- Analysis of the Lyapunov dimension and its correlation with incoherent oscillator populations.
- Analytical treatment of the linearized evolution operator in the thermodynamic limit.
Main Results:
- Numerical simulations reveal the hyperchaotic nature of chimera states.
- The Lyapunov dimension of chimera states shows a direct correspondence with the number of incoherent oscillators.
- Analytic results in the thermodynamic limit demonstrate neutral stability for chimera states.
- The continuous spectrum in the thermodynamic limit matches the limiting behavior of the hyperchaotic Lyapunov spectrum from finite systems.
Conclusions:
- Chimera states exhibit complex, hyperchaotic dynamics in finite systems, with stability linked to the degree of incoherence.
- The spectral analysis provides a bridge between finite-size system behavior and the thermodynamic limit, confirming neutral stability in the macroscopic regime.
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