Aggregated spots and waving loops in a reaction-advection-diffusion system with a global coupling.

We construct a phenomenological model describing aggregated spots and a loop structure. Our model is based on the Gray-Scott model which is supplemented with a global coupling term and advection terms. One of the species makes a field proportional to its concentration, which induces the advection. By numerically investigating the model, we show that the system has a transition from aggregated spots to a loop which wanders around chaotically or reaches a stationary state. Relation to a similar transition observed in a recent gas discharge experiment [S. Nasuno, Chaos 13, 3 (2003)] is discussed.