LIMIT CYCLE BIFURCATIONS OF A KIND OF LI&#201;NARD SYSTEM WITH A HYPOBOLIC SADDLE AND A NILPOTENT CUSP

Junmin Yang; Feng Liang

doi:10.11948/2015041

2015 Volume 5 Issue 3

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Junmin Yang, Feng Liang. LIMIT CYCLE BIFURCATIONS OF A KIND OF LIÉNARD SYSTEM WITH A HYPOBOLIC SADDLE AND A NILPOTENT CUSP[J]. Journal of Applied Analysis & Computation, 2015, 5(3): 515-526. doi: 10.11948/2015041

Citation:

Junmin Yang, Feng Liang. LIMIT CYCLE BIFURCATIONS OF A KIND OF LIÉNARD SYSTEM WITH A HYPOBOLIC SADDLE AND A NILPOTENT CUSP[J]. Journal of Applied Analysis & Computation, 2015, 5(3): 515-526. doi: 10.11948/2015041

LIMIT CYCLE BIFURCATIONS OF A KIND OF LIÉNARD SYSTEM WITH A HYPOBOLIC SADDLE AND A NILPOTENT CUSP

Junmin Yang^1,2,
Feng Liang³

1 College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050016, China;
2 Hebei Key Laboratory of Computational Mathematics and Applications, Shijiazhuang 050016, China;
3 College of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000, China

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Abstract

Abstract

This paper gives a general theorem on the number of limit cycles of a near Hamiltonian system with a heteroclinic loop passing through a hyperbolic saddle and a nilpotent cusp. Then we study a kind of Liénard systems of type (n, 4) for 3 ≤ n ≤ 27 and obtain the lower bound of the maximal number of limit cycles for this kind of system.
- limit cycle /
- Liénard system /
- nilpotent cusp /
- heteroclinic loop
MSC: 35D;35C

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References

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