Synchronizing spatio-temporal chaos with imperfect models: a stochastic surface growth picture
Diego Pazó1, Juan M López1, Rafael Gallego2
1Instituto de Física de Cantabria (IFCA), CSIC-Universidad de Cantabria, 39005 Santander, Spain.
Chaos (Woodbury, N.Y.)
|January 3, 2015
Summary
We investigated synchronization in imperfect dynamical systems. The synchronization error behaves like a rough surface described by the Kardar-Parisi-Zhang equation, showing generic results for various systems.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Statistical Physics
Background:
- Synchronization is crucial in many natural and engineered systems.
- Model imperfections, such as parameter mismatch and unresolved fast scales, challenge synchronization.
- Understanding these imperfections is key to predicting system behavior.
Purpose of the Study:
- To analyze the impact of model imperfections on the synchronization of spatially extended dynamical systems.
- To characterize the spatial distribution of synchronization error.
- To determine if the observed phenomena are generic across different systems and imperfection types.
Main Methods:
- Modeling two spatially extended dynamical systems with introduced imperfections.
- Analyzing the synchronization error across space.
- Comparing results for parameter mismatch and unresolved fast scales.
- Relating the synchronization error to the Kardar-Parisi-Zhang equation.
Main Results:
- Synchronization error can be visualized as a rough surface.
- This surface dynamics are governed by the Kardar-Parisi-Zhang equation with bounding walls.
- Both parameter mismatch and unresolved fast scales lead to the same qualitative synchronization error behavior.
- The findings are consistent across different system setups.
Conclusions:
- The Kardar-Parisi-Zhang equation effectively describes synchronization errors in imperfect systems.
- Model imperfections introduce nonlinearities and discrepancies affecting synchronization.
- The observed synchronization error dynamics are generic for a wide range of spatially extended systems.
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