Internal composite bound states in deterministic reaction diffusion models

Abstract

By identifying potential composite states that occur in the Sel'kov-Gray-Scott (GS) model, we show that it can be considered as an effective theory at large spatio-temporal scales, arising from a more \textit{fundamental} theory (which treats these composite states as fundamental chemical species obeying the diffusion equation) relevant at shorter spatio-temporal scales. When simulations in the latter model are performed as a function of a parameter $M = \lambda^{-1}$, the generated spatial patterns evolve at late times into those of the GS model at large $M$, implying that the composites follow their own unique dynamics at short scales. This separation of scales is an example of \textit{dynamical} decoupling in reaction diffusion systems.