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.　©　2021,　Editorial　Board　of　Journal　of　Vibration　Engineering.　All　right　reserved.