ON THE LIMIT CYCLES OF A KIND OF LI&#201;NARD SYSTEM WITH A NILPOTENT CENTER UNDER PERTURBATIONS

Junmin Yang

doi:10.11948/2012024

2012 Volume 2 Issue 3

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2012 > 2(3): 325-339

Next Article Previous Article

Junmin Yang. ON THE LIMIT CYCLES OF A KIND OF LIÉNARD SYSTEM WITH A NILPOTENT CENTER UNDER PERTURBATIONS[J]. Journal of Applied Analysis & Computation, 2012, 2(3): 325-339. doi: 10.11948/2012024

Citation:

Junmin Yang. ON THE LIMIT CYCLES OF A KIND OF LIÉNARD SYSTEM WITH A NILPOTENT CENTER UNDER PERTURBATIONS[J]. Journal of Applied Analysis & Computation, 2012, 2(3): 325-339. doi: 10.11948/2012024

ON THE LIMIT CYCLES OF A KIND OF LIÉNARD SYSTEM WITH A NILPOTENT CENTER UNDER PERTURBATIONS

Junmin Yang

College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050024, China

Fund Project:

Abstract

Abstract

In this paper, we study the number of limit cycles of a kind of Liénard system with a nilpotent center under perturbations. Let L(m, n) denote the maximal number of limit cycles of this Liénard system Ẍ=y-εF (x), ẏ=-g(x) near the origin, where m=deg g, n=deg F. We obtain some results on the lower bound of L(m, n) for m=4, 2 ≤ n ≤ 20, m=5; 2 ≤ n ≤ 10, m=6, 2 ≤ n ≤ 5 and m=7, 2 ≤ n ≤ 4, where some results are new.
- Nilpotent center /
- Liénard system /
- limit cycle
MSC: 35D;35C

FullText(HTML)

References

[1]	M. Han, J. Jiang and H. Zhu, Limit cycle bifurcations in near-Hamiltonian systmes by perturbing a nilpotent center, Int. J. Bifurcation and Chaos, 18(2008), 3013-3027. Google Scholar
[2]	M. Han, C. Shu, J. Yang and A. Chian, Polynomial Hamiltonian systems with a nilpotent critical point, J. Adv. Space Res., 46(2010), 521-525. Google Scholar
[3]	J. Llibre and X. Zhang, On the number of limit cycles for some perturbed Hamiltonian polynomial systems, Dyn. Contin. Discr. Impuls. Syst. Series A:Math. Anal., 8(2001), 161-181. Google Scholar
[4]	C. Li, W. Li, J. Llibre and Z. Zhang, Polynomial systems:A lower bound for the weakened 16th Hilbert problem, Extracta Math., 16(2001), 441-447. Google Scholar
[5]	J. Jiang and M. Han, Melnikov function and limit cycle bifurcation from a nilpotent center, Bull. Sci. math., 132(2008), 182-193. Google Scholar
[6]	J. Su, J. Yang and M. Han, Hopf bifurcation of Liénard systems by perturbing a nilpotent center, to appear in IJBC. Google Scholar