Turbulent fronts in resonantly forced oscillatory systems

Abstract

Phase fronts in the forced complex Ginzburg–Landau equation, a model of a resonantly forced oscillatory reaction–diffusion system, are studied in the 3:1 resonance regime. The focus is on the turbulent (Benjamin–Feir-unstable) regime of the corresponding unforced system; in the forced system, phase fronts between spatially uniform phase-locked states exhibit complex dynamics. In one dimension, for strong forcing, phase fronts move with constant velocity. As the forcing intensity is lowered there is a bifurcation to oscillatory motion, followed by a bifurcation to a regime in which fronts multiply ia the nucleation of domains of the third homogeneous phase in the front. In two dimensional systems, rough fronts with turbulent, complex internal structure may arise. For a critical value of the forcing intensity there is a nonequilibrium phase transition in which the turbulent interface grows to occupy the entire system. The phenomena we explore can be probed by experiments on periodically forced light sensitive reaction–diffusion systems.