Generic spatiotemporal dynamics near codimension-two Turing-Hopf bifurcations

The coupling of spatial and temporal symmetry breaking instabilities is studied in a two-variable reaction-diffusion model describing semiconductor transport. A variety of spatiotemporal patterns corresponding to pure Hopf and Turing modes, localized patterns, and mixed Turing-Hopf modes including subharmonic spatiotemporal spiking are found. By organizing the results in a time-scale versus space-scale diagram, and by comparing them with a chemical reaction-diffusion model, it is shown that such behavior is generic for a class of extended nonlinear dynamic systems near codimension-two Turing-Hopf bifurcations.