Bifurcation of Closed Orbit for a Class of C~r System

In this paper, the bifurcation of closed orbit for a class of C r system dx/dt=-y+x(x 2+y 2-1) k+λxf 1(x,y) dy/dt=x+y(x 2+y 2-1) k+λyf 2(x,y) is discussed. By using the zero point of the returned function, the uniqueness of limit cycle bifurcated from the simple limit cycle is obtained and for the detailed results, a sufficient condition is also obtained to guarantee that the multiple limit cycle can produce two limit cycles with f i(x,y) being given specially.