Front explosion in a resonantly forced complex Ginzburg–Landau system

Abstract

Periodically forced oscillatory reaction–diffusion systems near the Hopf bifurcation can be modeled by the resonantly forced complex Ginzburg–Landau equation. In the 3:1 resonant locking regime this equation has three stable fixed points corresponding to the phase-locked states in the underlying reaction–diffusion system. Phase fronts separate spatial domains containing the phase-locked states. When the Ginzburg–Landau equation parameters lie in the Benjamin–Feir-unstable regime, the phase fronts have a turbulent internal spatio-temporal structure. As the forcing intensity is changed, the intrinsic width of a front grows until, at a critical value, the front “explodes” and the turbulent interfacial zone expands to fill the entire domain. The scaling properties of this transition are explored and it is shown that front width and spatial and temporal correlations diverge as the critical forcing intensity is approached. These results are compared with similar behavior seen in a coupled map model with period-3 local dynamics. The prospects for observation of these phenomena in experiments on periodically forced reaction–diffusion systems are discussed.