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Spatiotemporal patterns are often modeled using reaction-diffusion equations,which combine complex reactions between constituents with ideal diffusivemotion. Such descriptions neglect physical interactions between constituents,which might affect resulting patterns. To overcome this, we study how physicalinteractions affect cyclic dominant reactions, like the seminalrock-paper-scissors game, which exhibits spiral waves for ideal diffusion.Generalizing diffusion to incorporate physical interactions, we find that weakinteractions change the length- and time-scales of spiral waves, consistentwith a mapping to the complex Ginzburg-Landau equation. In contrast, strongrepulsive interactions typically generate oscillating lattices, and strongattraction leads to an interplay of phase separation and chemical oscillations,like droplets co-locating with cores of spiral waves. Our work suggests thatphysical interactions are relevant for forming spatiotemporal patterns innature, and it might shed light on how biodiversity is maintained in ecologicalsettings.

Influence of physical interactions on spatiotemporal patterns