Planar Polynomial Systems with Non-Alsebraic Limit Cycles

摘要

n this paper, we study the existence of the non-algebraic limit cycles of the systemsrndx/dt = P_n(x,y)+xR_m(x,y) dy/dt = Qn{x,y)+yR_m{x,y)rnwhere P_n(x,y), Q_n(x,y) and R_m(x,y) are homogeneous polynomials of degrees n, n and m respectively with n < m and n is odd, m is even. We apply this theorem to determine conditions for the existence of the non-algebraic limit cycles of certain family of planar systems The tool for proving these results is based on a method developed in [7].