In　order　to　investigate　the　global　characteristics　of　dynamic　solutions　of　gear　systems,　a　nonlinear　dynamical　model　of　the　power-split　spur　gear　transmission　is　established,　and　the　calculation　algorithm　regarding　global　solutions　under　main　excitation　parameters　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.　©　2021,　Editorial　Board　of　Journal　of　Vibration　Engineering.　All　right　reserved.