QUASI-PERIODIC WAVES ALONG A PULSATING PROPAGATING FRONT IN A REACTION-DIFFUSION SYSTEM.

The authors consider a system of reaction-diffusion equations for which there exists a solution with a uniformly propagating front, and from which solutions describing a pulsating propagating front with periodic traveling and standing waves along the front, bifurcate supercritically. They construct a pulsating propagating solution branch, with quasi-periodic traveling waves along its front, which connects the periodic traveling and standing wave branches. Thus the quasi-periodic branch arises as a secondary bifurcation from the uniformly propagating solution. Their construction involves a perturbation analysis in the neighborhood of a certain degenerate point in parameter space. The stability of the various solution branches is investigated.