In order to investigate the global characteristics of dynamic solutions of gear systems，a nonlinear dynamical model of thepower-split spur gear transmission is established，and the calculation algorithm regarding global solutions under main excitation pa?rameters is deduced based on cell mapping method（CMM）as well as domain decomposition method（DDM）. Parametric planar solution domains constructed by damping ratio respectively with synthetically transmission error，mesh frequency and backlash are computed，and the potential global evolution behaviors within solution domains are exhibited，such as period-doubling bifurcation cascades，chaotic window zones. The bifurcation routes inside solution domain with respect to varied error magnitudes are tracked by applying largest Lyapunov exponent，which demonstrate that bifurcation nodes are in consistent with the subdomain boundary points presented in parameterized solution domain. By numerically calculating the global behaviors of the basin of attraction under multiple damping ratios，it is shown that mutual expansion and retrogression between the chaotic basin of attraction and the period 1 basin of attraction are remarkably，and the local equilibrium of the cells nearby the boundary is extremely unstable. The basin of attraction is sensitively while the damping ratio reaches 0.04，and multiple attractors coexisting phenomenon exhibits significantly.The result could provide references for vibration optimization or even global design of dynamic parameters for gear system.