  Turing bifurcation and Hopf bifurcation are two important kinds of
transitions giving birth to inhomogeneous solutions, in spatial or temporal
ways. On a disk, these two bifurcations may lead to equivariant Turing-Hopf
bifurcations. In this paper, normal forms for three kinds of Turing-Hopf
bifurcations are given and the breathing, standing wave-like, and rotating
wave-like patterns are found in numerical examples.
