5 research outputs found
On the number of limit cycles of the Lienard equation
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.Comment: 10 pages, 5 figures. Submitted to Physical Review
Variational approach to a class of nonlinear oscillators with several limit cycles
We study limit cycles of nonlinear oscillators described by the equation
. Depending on the nonlinearity this equation
may exhibit different number of limit cycles.
We show that limit cycles correspond to relative extrema of a certain
functional. Analytical results in the limits and are
in agreement with previously known criteria. For intermediate numerical
determination of the limit cycles can be obtained.Comment: 12 pages, 3 figure