Simple model for synchronization of two Belousov–Zhabotinsky gels interacting mechanically

A Belousov–Zhabotinsky (BZ) gel is a unique biomimetic system that undergoes autonomous volume oscillations induced by the redox oscillation of the BZ reaction. In a previous study, researchers reported that the oscillations of two BZ gels coupled by compression were synchronized by a mechanical interaction. They mathematically explained the synchronization behavior using a phase oscillator model. As a different approach to the previous study, a physicochemical investigation of the phenomenon will lead to a better understanding of the functional biological rhythms essential for life. In this study, we construct a simple phenomenological model to understand the synchronization of BZ gels. The model consists of two parts. One is the dynamics of the chemical reactions in the BZ gels. We use a phenomenological model based on the Oregonator for the BZ reaction. The other is the dynamics of the mechanical deformation of the BZ gel. Using approximations, we extract the parameters essential for the synchronization of a mechanical interaction. Thus, we can derive a novel equation for the deformation dynamics of mechanically coupled BZ gels. By combining these two parts, we perform numerical calculations. This allows us to find that the synchronization of the two BZ gels is less likely to occur under stronger compression. We explain this trend through one physicochemical parameter in our model: the volume fraction of the BZ gel in the reduced state.