Internal Composite Bound States in Deterministic Reaction Diffusion Models

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 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 = λ^-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 dynamical decoupling in reaction diffusion systems.