Spatio{temporal Dynamics near a Supercritical Turing{hopf Bifurcation in a Two{dimensional Reaction{diiusion System

Pattern formation in semiconductor heterostructures is studied on the basis of a spatially two{dimensional model of reaction{diiusion type. In particular, we investigate the neighbourhood of a codimension{two Turing{Hopf instability by analytical methods. Amplitude equations are derived which predict the absence of mixed modes but extended ranges of bistability between homogeneous oscillatory states and hexagonal Turing patterns. Our results are connrmed by numerical simulations. The features are not connned to a neighbourhood of the bifurcation point so that the conclusions of the weakly nonlinear analysis explain the observations in large portions of the parameter space at least qualitatively