Abstract: In engineering and technology, it is often demanded that self-oscillation.be eliminated . 50 that the equipment or machinery may not be damaged. In this paper, a mathematical model for reducing vibration is given by the following equations:x₁+φ(x₁)+k₁(x₁-x₂)=0,x₂+cx₁+k₂(x₂-x₁)=0 (*)We have discussed how to choose suitable parameters c₁, k₁, k₂ of equations (*), so as to make the zero solution to be of global stability. Several theorems on the global stability of the zero solution of equations (*)are also given.

Key words: bifurcation, chaos, large amplitude, nonlinear