Abstract: Magnetorheological (MR) fluids is a kind of smartmaterials, it can be transformed from Newton fluids into visco-plastic solidby varying the strength of the magnetic field. The dampers made by MR fluidshave a number of attractive features, for example, inexpensive tomanufacture, small power requirements, reliability, stability, and cancontinually change its state. The process of change is very quick, less thana few milliseconeds, and can be easily controlled. MR dampers have beenrecognized as having many attractive characteristics for use in vibrationcontrol applications, it is a kind of ideal semi-active control devices. MRdamper is widely used in the civil engineering, vehicle suspension systemand its structural characteristics have been extensively studied. But, up tonow, the dynamic behaviors about MR damper semi-active control system,specially, its bifurcation behaviors and global dynamics have not beendiscussed.The problem of bifurcation behavior for the MR damper nonlinear system isdiscussed. A dynamic model of the system with nonlinear MR damper force ispresented. The system's normal form and universal unfolding of the doublezero eigenvalue are achieved. The complex dynamic behavior of the nonlinearsystem will be shown by the analysis. By theoretical analysis, it is shownthat the design of parameters has a close relation with the system'sstability; the range of selected parameters are achieved when the system isstable, based on the condition of bifurcation parameters, bifurcation curve,bifurcation set and phase portraits. From numerical simulating analysis, thecomplex dynamics behavior is shown, and the result is in correspondence withthe theoretic analysis.