In　this　paper,　the　nonlinear　and　dual-parameter　chaotic　vibrations　are　investigated　for　the　blisk　structure　with　the　lumped　parameter　model　under　combined　the　aerodynamic　force　and　varying　rotating　speed.　The　varying　rotating　speed　and　aerodynamic　force　are,　respectively,　simplified　to　the　parametric　and　external　excitations.　The　nonlinear　governing　equations　of　motion　for　the　rotating　blisk　are　established　by　using　Hamilton＇s　principle.　The　free　vibration　and　mode　localization　phenomena　are　studied　for　the　tuning　and　mistuning　blisks.　Due　to　the　mistuning,　the　periodic　characteristics　of　the　blisk　structure　are　destroyed　and　uniform　distribution　of　the　energy　is　broken.　It　is　found　that　there　is　a　positive　correlation　between　the　mistuning　variable　and　mode　localization　factor　to　exhibit　the　large　vibration　of　the　blisk　in　a　certain　region.　The　method　of　multiple　scales　is　applied　to　derive　four-dimensional　averaged　equations　of　the　blisk　under　1:1　internal　and　principal　parametric　resonances.　The　amplitude-frequency　response　curves　of　the　blisk　are　studied,　which　illustrate　the　influence　of　different　parameters　on　the　bandwidth　and　vibration　amplitudes　of　the　blisk.　Lyapunov　exponent,　bifurcation　diagrams,　phase　portraits,　waveforms　and　Poincare　maps　are　depicted.　The　dual-parameter　Lyapunov　exponents　and　bifurcation　diagrams　of　the　blisk　reveal　the　paths　leading　to　the　chaos.　The　influences　of　different　parameters　on　the　bifurcation　and　chaotic　vibrations　are　analyzed.　The　numerical　results　demonstrate　that　the　parametric　and　external　excitations,　rotating　speed　and　damping　determine　the　occurrence　of　the　chaotic　vibrations　and　paths　leading　to　the　chaotic　vibrations　in　the　blisk.