On the number of limit cycles of the Lienard equation

Details On the number of limit cycles of the Lienard equation On the number of limit cycles of the Lienard equation

1997-04-30

arxiv.org/abs/chao-dyn/9705006v1

Nonlinear Sciences

Chaotic Dynamics

10 pages, 5 figures. Submitted to Physical Review E

Scientific paper

10.1103/PhysRevE.56.3809

In this paper, we study a Lienard system of the form dot{x}=y-F(x), dot{y}=-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.

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