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Extensive and subextensive chaos in globally coupled dynamical systems
Kazumasa A Takeuchi1, Hugues Chaté, Francesco Ginelli
1Service de Physique de l'État Condensé, CEA-Saclay, F-91191 Gif-sur-Yvette, France.
Physical Review Letters
|October 27, 2011
Summary
Chaos in globally coupled dynamical systems exhibits both extensive and subextensive properties. The spectrum of Lyapunov exponents shows a flat band, but also subextensive bands with unique scaling behavior.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Statistical Physics
Background:
- Globally coupled identical dynamical systems are fundamental models in physics.
- Understanding the nature of chaos, including its extensivity, is crucial for characterizing complex system behavior.
Purpose of the Study:
- To investigate the properties of chaos in globally coupled identical dynamical systems.
- To determine if chaos in these systems is extensive, subextensive, or both.
Main Methods:
- Employed a combination of analytical and numerical techniques.
- Analyzed the spectrum of Lyapunov exponents for varying system sizes.
Main Results:
- Chaos in these systems is shown to be both extensive and subextensive.
- The Lyapunov exponent spectrum is asymptotically flat (extensive) at λ(0).
- Subextensive bands with O(logN) exponents exhibit scaling behavior: λ≃λ(∞)+c/logN, where λ(∞)≠λ(0).
Conclusions:
- Chaos in globally coupled systems displays a dual nature of extensivity and subextensivity.
- The observed Lyapunov exponent scaling provides new insights into the structure of chaotic states in large systems.
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