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Spirals in a reaction-diffusion system: Dependence of wave dynamics on excitability
Dhriti Mahanta1, Nirmali Prabha Das1, Sumana Dutta1
1Department of Chemistry, Indian Institute of Technology Guwahati, Guwahati 781039, India.
Physical Review. E
|March 18, 2018
Summary
The excitability of the Belousov-Zhabotinsky (BZ) reaction influences spiral wave properties. Increasing excitability (ε) decreases wave frequency and expands spiral core dimensions, confirmed by experiments.
Area of Science:
- Chemical kinetics
- Nonlinear dynamics
- Pattern formation
Background:
- The Belousov-Zhabotinsky (BZ) reaction is a classic example of a chemical oscillating system exhibiting complex spatiotemporal patterns.
- Spiral waves are a common emergent behavior in excitable media, including the BZ reaction.
- Understanding the factors that control spiral wave dynamics is crucial for comprehending pattern formation in chemical and biological systems.
Purpose of the Study:
- To investigate the impact of excitability on the properties of spiral waves in the Belousov-Zhabotinsky (BZ) reaction.
- To explore the relationship between the excitability parameter (ε) and wave dynamics, including frequency, core dimension, and trajectory.
- To validate numerical findings with experimental observations in thin-layer BZ systems.
Main Methods:
- Numerical simulations using the Oregonator model to explore various excitability regimes and Hopf bifurcations.
- Experimental investigation of thin-layer BZ reactions with controlled variations in reactant concentrations to alter excitability.
- Quantitative analysis of spiral wave properties such as frequency, wavelength, and tip trajectory.
Main Results:
- A Hopf bifurcation was identified, leading to different wave activity regimes from sustained oscillations to wave damping.
- Increased excitability (ε) resulted in an exponential decrease in wave frequency and an expansion of the spiral core dimension.
- Experimental results quantitatively confirmed the numerical predictions regarding the influence of excitability and substrate concentrations on spiral wave behavior, including drifting and meandering patterns.
Conclusions:
- Excitability is a critical parameter governing spiral wave dynamics in the BZ reaction.
- The study provides quantitative evidence linking the excitability parameter (ε) to substrate concentrations and spiral wave properties.
- Findings contribute to a deeper understanding of pattern formation and control in excitable chemical systems.
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