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Spatiotemporal chaos arising from standing waves in a reaction-diffusion system with cross-diffusion.
Igal Berenstein1, Carsten Beta
1Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam, Germany. berenst@uni-potsdam.de
The Journal of Chemical Physics
|January 28, 2012
Summary
Quasi-standing wave patterns emerge in the Belousov-Zhabotinsky reaction
Area of Science:
- Chemical kinetics
- Nonlinear dynamics
- Pattern formation
Background:
- The Belousov-Zhabotinsky reaction is a classic example of a chemical oscillator.
- Understanding pattern formation in chemical systems is crucial for various applications.
- Previous models often required wave instability to generate complex patterns.
Purpose of the Study:
- To investigate the emergence of standing wave patterns in the Oregonator model.
- To explore the role of cross-diffusion in pattern formation.
- To analyze the influence of system size on wave dynamics.
Main Methods:
- Utilized the two-variable Oregonator model.
- Incorporated a cross-diffusion term into the model.
- Simulated the system across a range of system sizes.
Main Results:
- Quasi-standing wave patterns were observed without requiring wave instability.
- These standing waves exhibited half the frequency of bulk oscillations.
- System size influenced pattern regularity, leading to regular, irregular, and chaotic states.
Conclusions:
- Cross-diffusion can induce standing wave patterns in the Oregonator model.
- System size is a critical parameter controlling the complexity of observed patterns.
- The study reveals a transition from regular standing waves to spatiotemporal chaos.
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