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Resonant-pattern formation induced by additive noise in periodically forced reaction-diffusion systems
Hongli Wang1, Ke Zhang, Qi Ouyang
1Department of Physics, Peking University, Beijing 100871, People's Republic of China.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 10, 2006
Summary
Additive noise in a Brusselator model generates resonant patterns like hexagons and stripes. Colored noise is crucial for sustaining these frequency-locked patterns, which oscillate at half the forcing frequency.
Area of Science:
- Nonlinear dynamics
- Chemical kinetics
- Pattern formation
Background:
- Reaction-diffusion systems exhibit complex dynamics under external forcing.
- The Brusselator model is a classic example of a system capable of exhibiting oscillations and pattern formation.
- Additive noise can significantly alter the behavior of nonlinear systems.
Purpose of the Study:
- To investigate the role of additive noise in inducing frequency-locked resonant patterns in a periodically forced Brusselator model.
- To characterize the types of patterns formed and the conditions under which they are sustained.
- To explore the relationship between noise properties (strength, correlation time) and pattern dynamics.
Main Methods:
- Numerical simulations of the periodically forced Brusselator model with additive noise.
- Analysis of spatio-temporal patterns and their frequency spectra.
- Comparison with the behavior of the corresponding forced complex Ginzburg-Landau equation.
Main Results:
- Additive noise, specifically colored noise (spatially white, temporally correlated), induces resonant patterns (hexagons, stripes, labyrinths) in the 2:1 frequency-locking regime.
- Pattern formation is controlled by noise strength and temporal correlation time, with transitions observed from homogeneous states to various patterns as noise strength increases.
- Sustained, frequency-locked patterns require colored noise with finite temporal correlation; white noise leads to irregular, near-resonant patterns.
- The observed phenomenon corresponds to noise-induced Turing instability in the forced complex Ginzburg-Landau equation.
Conclusions:
- Colored additive noise can generate and sustain frequency-locked resonant patterns in periodically forced reaction-diffusion systems.
- The characteristics of the noise, particularly its temporal correlation, are critical for the formation of ordered, resonant patterns.
- This study provides insights into noise-induced instabilities and pattern formation in nonlinear systems, with implications for understanding complex phenomena in physics and chemistry.
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