  Competition of spatial and temporal instabilities under time delay near the
codimension-two Turing-Hopf bifurcations is studied in a reaction-diffusion
equation. The time delay changes remarkably the oscillation frequency, the
intrinsic wave vector, and the intensities of both Turing and Hopf modes. The
application of appropriate time delay can control the competition between the
Turing and Hopf modes. Analysis shows that individual or both feedbacks can
realize the control of the transformation between the Turing and Hopf patterns.
Two dimensional numerical simulations validate the analytical results.
