Resonant spatio-temporal forcing of oscillatory media

An extension of the complex Ginzburg-Landau equation describing resonant spatio-temporal forcing of oscillatory media is investigated. Periodic forcing in space and time leads to spatial structures with two different symmetries: harmonic patterns with the same and subharmonic patterns with twice the wavelength of the external forcing. A linear stability analysis of the homogeneous state carried out analytically leads to subharmonic patterns for intermediate forcing strength, while harmonic modes prevail for very weak and strong forcing amplitudes. Numerical simulations confirm the analytical predictions for weak forcing and show coexistence between the two types of patterns beyond threshold. In addition, traveling localized patterns such as phase flips in subharmonic patterns and traveling patches of subharmonic patterns in a harmonic background have been discovered. In the parameter range of Benjamin-Feir turbulence, stable subharmonic patterns occur upon forcing, which undergo a transition scenario back to irregular dynamics for increasing values of the control parameter