The number of limit cycles of cubic Hamiltonian system with perturbation

Nonlinear Analysis: Real World Applications

Volumn 7, Issue 5, 2006, Pages 943-949

  Wu, Cheng qiang ^a   Xia, Yonghui ^a  

^a FUZHOU UNIVERSITY   (China)

Author keywords

Hamiltonian system; Limit cycle; Perturbed system; Stability

Indexed keywords

NONLINEAR SYSTEMS; PERTURBATION TECHNIQUES; POLYNOMIALS; STABILITY;

CUBIC HAMILTONIAN SYSTEM; HAMILTONIAN SYSTEM; LIMIT CYCLE; PERTURBED SYSTEM;

HAMILTONIANS;

EID: 33745116563     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2006.02.002     Document Type: Article

References (9)

1. Arnold V.I. Loss of stability of self-oscillation close to resonance and versal deformations of equivalent vector fields. Funct. Anal. Appl. 11 (1977) 1-10
2. Han M. On the number and distributions of limit cycles in a cubic system. China Ann. Math. 23A 2 (2002) 143-152
3. Iliev I.D., and Perko I.M. High order bifurcations of limit cycles. J. Differential Equations 154 (1999) 339-363
4. Li J. Hilbert's 16th problem and bifurcations of planar polynomial vector fields. International J. Bifurcation Chaos 13 1 (2003) 47-106
5. Li C.Z., G. W., Llibre J., et al. Polynomial systems: a lower bound for the weakened 16th Hilbert problem. Extracte Math. 16 3 (2001) 441-447
6. Song Y. The Poincaré bifurcation of cubic Hamiltonian systems with a global center. Acta Math. Sin. 47 2 (2004) 291-298 (in Chinese)
7. Yang C.X., and Wang R.Q. Number and location of limit cycles in a class of perturbed polynomial systems. Acta Math. Appl. Sin. (English Series) 20 1 (2004) 155-166
8. Ye Y.Q. The theory of limit cycles. Transactions on Mathematical Monographs vol. 66 (1986), American Mathematical Society, New York
9. Y.L. Zhao, Abelian integrals for cubic Hamilton vector fields, The Doctoral Thesis in Peking University, 1998.