Spatiotemporal dynamics near a supercritical Turing-Hopf bifurcation in a two-dimensional reaction-diffusion system - art. no. 026219

Pattern formation in semiconductor heterostructures is studied on the basis of a spatially two-dimensional model of reaction-diffusion type. In partic ular, we investigate the neighborhood of a codimension-two Turing-Hopf inst ability by analytical methods. Amplitude equations are derived which predic t the absence of mixed modes but extended ranges of bistability between hom ogeneous oscillatory states and hexagonal Turing patterns. Our results are confirmed by numerical simulations. The features are not confined to a neig hborhood of the bifurcation point so that the conclusions of the weakly non linear analysis explain the observations in large portions of the parameter space at least qualitatively.