Based on the comprehensive analysis of the basic dynamic characters of the coupled dynamos system, we have calculated the Lyapunov exponent spectra, bifurcation diagrams and so on, and discussed the chaotic bifurcation and mutative characteristic thoroughly in the periodic windows of the system, and the dual-parameter characteristic is also analyzed. It is found that a boundary line is absent in period-doubling bifurcations and a complicated bifurcation structure appears in 2D parameter space, the influences of two control parameters to the dynamic behavior are different.