Number of limit cycles of the Lienard equation

摘要

In this paper, we study a Lienard system of the form (x) over dot = y - F(x), (y) over dot = -x, where F(x) is an odd polynomial. We introduce a method that gives a sequence of algebraic approximations to the equation of each Limit cycle of the system. This sequence seems to converge to the exact equation of each limit cycle. We obtain also a sequence of polynomials R-n(x) whose roots of odd multiplicity are related to the number and location of the limit cycles of the system.