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Published on: August 5, 2013
Resonant suppression of Turing patterns by periodic illumination
M Dolnik1, A M Zhabotinsky, I R Epstein
1Department of Chemistry and Volen Center for Complex Systems, Brandeis University, Waltham, Massachusetts 02454-9110, USA.
Summary
We investigated how periodic illumination suppresses Turing patterns in a chemical reaction. Resonance occurs at the system
Area of Science:
- Chemical kinetics
- Nonlinear dynamics
- Pattern formation
Background:
- Turing patterns are spatial structures arising from reaction-diffusion systems.
- Periodic forcing can alter the dynamics of chemical reactions.
- The chlorine dioxide-iodine-malonic acid reaction is a well-studied oscillating chemical system.
Purpose of the Study:
- To investigate resonant behavior in Turing pattern suppression.
- To understand the effect of periodic illumination on pattern formation.
- To compare different forcing waveforms and analyze coupled systems.
Main Methods:
- Numerical simulations of partial differential equations.
- Analysis of autonomous oscillations in well-stirred systems.
- Bifurcation analysis using numerical continuation for coupled cells.
Main Results:
- Resonance in Turing pattern suppression was observed at the frequency of autonomous oscillations.
- Suppression is sharper at lower complexing agent concentrations.
- Square wave forcing is more effective than sinusoidal forcing.
- Bifurcation analysis accurately predicts resonance boundaries in coupled systems.
Conclusions:
- Periodic illumination can resonantly suppress Turing patterns.
- Forcing waveform and concentration significantly impact suppression.
- Coupled cell dynamics provide insights into resonance phenomena.
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