The dynamical behavior of laser Ginzburg-Landau equation, which describes the sponta-neously spacial temporal symmetry breaking, has been investigated, In the case of inhomoge-neous stationary solution, it shows the cooperative frequency locking; and in the case of spa-tial-temporal oscillatory solution, all the transverse modes have a common optical carrier fre-quency. However, a chaotic solution can be generated at lower pumping, due to the diffraction of electro-magnetic field and nonlinearity. The numerical results show that, in the situation of small detuning, the reduced phase diffusion equation of this model can more precisely du-plicate its global dynamical behavior. It illustrates that the phase pattern of field guides the dy-namics in spontaneous formation of the transverse pattern of field.
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