Interaction of multiple spiral rotors in a reaction-diffusion system

TL;DR

This paper investigates how multiple spiral rotors in reaction-diffusion systems interact, revealing attraction, repulsion, and annihilation behaviors through simulations and experiments, advancing understanding of excitable media dynamics.

Contribution

It provides a quantitative analysis of spiral rotor interactions and validates findings with experimental results, offering new insights into rotor dynamics in reaction-diffusion systems.

Findings

Identified critical distances for rotor attraction and repulsion.

Demonstrated annihilation of spirals at close proximity.

Validated numerical results with Belousov-Zhabotinsky experiments.

Abstract

Rotors of reaction and diffusion, that revolve around a circular singularity, and the corresponding spiral wave activity around it, influence the nature of several excitable media. Their dynamics are known to be affected by target waves and external gradients. When the core of two spirals come very close to each other, they could either repel or attract, depending on their relative chirality and the distance separating them. Multiple pairs of spiral waves, in close vicinity, could alter the paths of the individual rotors. A single spiral core, will be influenced most by the rotor closest to it, or linked to it by a common wave. If within a limiting distance, they would attract each other, and annihilate. Else, they will push each other away, until they reach a critical distance, beyond which, all interactions seem to cease. We have carried out numerical simulations based on a reaction-diffusion model to show the possible interactions of multiple spiral rotors. We are able to find a quantitative measurement of the distances determining the kind of interaction. Some unique dynamics is also unraveled. Experiments with the Belousov-Zhabotinsky reaction have successfully demonstrated the validity of our numerical results.