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Dynamics of perturbations in disordered chaotic systems
Ivan G Szendro1, Juan M López, Miguel A Rodríguez
1Instituto de Física de Cantabria (IFCA), CSIC-UC, E-39005 Santander, Spain. szendro@ifca.unican.es
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2008
Summary
Random perturbations in chaotic systems with disorder localize around pinning centers. This localization leads to self-organized structures with scale-invariant correlations, revealing three universality classes for error propagation.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Statistical Physics
Background:
- Spatially extended chaotic systems exhibit complex spatiotemporal behavior.
- Quenched disorder introduces randomness that significantly impacts system dynamics.
- Understanding error propagation is crucial for predicting system stability and behavior.
Purpose of the Study:
- To investigate the time evolution of perturbations in chaotic systems with quenched disorder.
- To analyze the localization and spatiotemporal behavior of perturbations.
- To identify universality classes governing error propagation in such systems.
Main Methods:
- Numerical simulations of disordered lattices of coupled chaotic elements.
- Analysis using the Hopf-Cole transform for spatiotemporal dynamics.
- Scaling analysis of critical roughening exponents.
Main Results:
- Perturbations exponentially localize in space around static pinning centers.
- The transformed perturbation surface self-organizes into a faceted structure with scale-invariant correlations.
- Three distinct universality classes for error propagation were identified, linked to disorder symmetries.
Conclusions:
- Disordered chaotic systems exhibit localization phenomena driven by pinning centers.
- Scale-invariant structures and distinct universality classes characterize error propagation.
- A phenomenological stochastic field theory offers insights for generalizing these findings to broader disordered systems.
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