In　this　two-part　paper,　we　investigate　nonlinear　dynamics　in　the　rotor-active　magnetic　bearings　(AMB)　system　with　8-pole　legs　and　the　time-varying　stiffness.　The　model　of　parametrically　excited　two-degree-of-　freedom　nonlinear　system　with　the　quadratic　and　cubic　nonlinearities　is　established　to　explore　the　periodic　and　quasiperiodic　motions　as　well　as　the　bifurcations　and　chaotic　dynamics　of　the　system.　The　method　of　multiple　scales　is　used　to　obtain　the　averaged　equations　in　the　case　of　primary　parameter　resonance　and　1/2　subharmonic　resonance.　In　Part　I　of　the　companion　paper,　numerical　approach　is　applied　to　the　averaged　equations　to　find　the　periodic,　quasiperiodic　solutions　and　local　bifurcations.　It　is　found　that　there　exist　2-period,　3-period,　4-period,　5-period,　multi-period　and　quasiperiodic　solutions　in　the　rotor-AMB　system　with　8-pole　legs　and　the　time-varying　stiffness.　The　catastrophic　phenomena　for　the　amplitude　of　nonlinear　oscillations　are　first　observed　in　the　rotor-AMB　system　with　8-pole　legs　and　the　time-varying　stiffness.　The　procedures　of　motion　from　the　transient　state　chaotic　motion　to　the　steady　state　periodic　and　quasiperiodic　motions　are　also　found.　The　results　obtained　here　show　that　there　exists　the　ability　of　auto-controlling　transient　state　chaos　to　the　steady　state　periodic　and　quasiperiodic　motions　in　the　rotor-AMB　system　with　8-pole　legs　and　the　time-varying　stiffness.