Comment on "Lienard systems, limit cycles, and Melnikov theory"

In papers by Sanjuan [Phys. Rev. E 57, 340 (1998)] and Giacomini and Neukir ch [Phys Rev. E 56, 3809 (1997)] Lienard systems of the form x = y- epsilon F(x, mu), Y = -x are studied. Sanjuan compares the results given by Melnik ov theory with the results given by the R-n polynomials in the paper by Gia comini and Neukirch and conjectures that the roots of the R-n polynomials t end toward the roots of the Melnikov polynomial when n -->infinity, for arb itrary values of epsilon. We show here that this is true only when epsilon --> 0 and that this fact strengthens the conjecture proposed by Giacomini a nd Neukirch.