To explore the basic conduction between parameters and dynamic characteristics of gear system，a nonlinear dynamical model of power combining spiral bevel gear system（SBGs）with multiple excitations are formulated. Some groups of two-dimensional parameterized solution domain structure are investigated and numerical calculated by cell mapping method（CMM）and domain decomposition method（DDM），the algorithm is based on the point mapping criterion of attractor on Poincaré section. With the bifurcation diagram and maximum Lyapunov exponent（MLE），the stable state characteristic is inspected，the result demonstrates that additional transmission error excitation can alter partial branch of period trajectory to shrink and transform on the path of meshing frequency bifurcation. The evolution of solution domains is solved when the comprehensive transmission error as well as damping ratio is combined with other parameters respectively，the responses such as periodic domains，chaotic bands and even cells on boundary zone are computed，the global behavior of periodic bifurcation inside the parameter domain is analyzed，and the distribution of variety subdomains in the solution domain structure is verified by applying MLE and Poincaré section.