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Microextensive chaos of a spatially extended system
Shigeyuki Tajima1, Henry S Greenside
1Department of Physics, Duke University, Durham, North Carolina 27708-0305, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2002
Summary
Dynamical complexity in chaotic systems increases with system size. The Lyapunov fractal dimension grows linearly with system size L, even for small increments, suggesting complexity can be enhanced without large size increases.
Area of Science:
- Nonlinear dynamics
- Chaos theory
- Statistical physics
Background:
- The Kuramoto-Sivashinsky equation models spatio-temporal chaos.
- Understanding how system size affects chaotic dynamics is crucial.
Purpose of the Study:
- To investigate the scaling of Lyapunov fractal dimension (D) with system size (L) in the one-dimensional Kuramoto-Sivashinsky equation.
- To determine if microextensivity of D holds for small system size increments.
Main Methods:
- Numerical analysis of chaotic states for the Kuramoto-Sivashinsky equation.
- System sizes L were analyzed in the range 79 ≤ L ≤ 93.
- Calculation of the Lyapunov fractal dimension D.
Main Results:
- The Lyapunov fractal dimension D was found to scale microextensively.
- D increased linearly with system size L.
- This linear increase was observed even for small increments ΔL compared to cell size and correlation lengths.
Conclusions:
- Spatially homogeneous chaotic systems can increase dynamical complexity by increasing system size, even by small amounts.
- Microextensivity of the Lyapunov fractal dimension is a significant finding for understanding chaotic system behavior.
- The results challenge traditional notions of characteristic size increases for enhanced complexity.
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