Limit cycle bifurcations of some Liénard systems

Journal of Mathematical Analysis and Applications

Volumn 366, Issue 1, 2010, Pages 242-255

  Yang, Junmin ^a   Han, Maoan ^a   Romanovski, Valery G ^b  

^a SHANGHAI NORMAL UNIVERSITY   (China)

^b UNIVERSITY OF MARIBOR   (Slovenia)

Author keywords

Bifurcation; Double homoclinic loop; Limit cycle; Polynomial system

Indexed keywords

EID: 75749158453     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2009.12.035     Document Type: Article

References (19)

1. Christopher C.J., and Lynch S. Small-amplitude limit cycles in polynomial Lienard systems with quadratic or cubic damping or restoring forces. Nonlinearity 12 (1999) 1099-1112
2. Dumortier F., and Li C. Perturbation from an elliptic Hamiltonian of degree four-IV figure eight-loop. J. Differential Equations 188 (2003) 512-554
3. Dumortier F., Panazzolo D., and Roussarie R. More limit cycles than expected in Lienard equations. Proc. Amer. Math. Soc. 135 (2007) 1895-1904
4. Han M. Liapunov constants and Hopf cyclicity of Lienard systems. Ann. Differential Equations 15 (1999) 113-126
5. Han M. On Hopf cyclicity of planar systems. J. Math. Anal. Appl. 245 (2000) 404-422
6. Han M. The number and distributions of limit cycles in a cubic system. Chinese Ann. Math. Ser. A 23 (2002) 143-152
7. Han M., Yang J., Tarta A., and Gao Y. Limit cycles near homoclinic and heteroclinic loops. J. Dynam. Differential Equations 20 (2008) 923-944
8. Han M., Yang J., and Yu P. Hopf bifurcations for near-Hamiltonian systems. Internat. J. Bifur. Chaos 19 12 (2009)
9. Han M., and Ye Y. On the coefficients appearing in the expansion of Melnikov functions in homoclinic bifurcations. Ann. Differential Equations 14 (1998) 156-162
10. Han M., Wang Z., and Zang H. Limit cycles by Hopf and homoclinic bifurcations for near-Hamiltonian systems. Chinese J. Contemp. Math. 28 (2007) 423-434
11. Han M., and Zhang T. Some bifurcation methods of finding limit cycles. Math. Biosci. Eng. 3 (2006) 67-77
12. Hou Y., and Han M. Melnikov functions for planar near-Hamiltonian systems and Hopf bifurcations. J. Shanghai Normal Univ. Nat. Sci. 35 (2006) 1-10
13. Li J. Hilbert's 16th problem and bifurcations of planar polynomial vector fields. Internat. J. Bifur. Chaos 13 (2003) 47-106
14. Lienard A. Étude des oscillations entrenues. Revue. Génerale de l'Électricité 23 (1928) 946-954
15. Lloyd N.G., and Pearson J.M. Symmetry in planar dynamical systems. J. Symbolic Comput. 33 (2002) 357-366
16. Shang D., and Han M. The global bifurcation of a kind of fifth system. Math. Appl. 18 (2005) 580-587
17. Yang J., and Han M. Limit cycles near a double homoclinic loop. Ann. Differential Equations 23 (2007) 536-545
18. Yang J., and Han M. On the number of limit cycles of a cubic near-Hamiltonian system. Discrete Contin. Dyn. Syst. 24 3 (2009) 827-840
19. Yu P., and Han M. Limit cycles in generalized Liénard systems. Chaos Solitons Fractals 30 (2006) 1048-1068