GENERIC SPATIOTEMPORAL DYNAMICS NEAR CODIMENSION-2 TURING-HOPF BIFURCATIONS

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