On Hopf cyclicity of planar systems

Journal of Mathematical Analysis and Applications

Volumn 245, Issue 2, 2000, Pages 404-422

  Han, Maoan ^a  

^a SHANGHAI JIAO TONG UNIVERSITY   (China)

Author keywords

Limit cycle; Hopf bifurcation; cyclicity

Indexed keywords

EID: 0034656493     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.2000.6758     Document Type: Article

References (18)

1. Bautin N. On the number of limit cycles which appear by variation of coefficients from an equilibrium position of focus or center type. Trans. Amer. Math. Soc. 100:1954;181-196.
2. Blows T. R., Lloyd N. G. The number of small-amplitude limit cycles of Lienard equations. Math. Proc. Cambridge Philos. Soc. 95:1984;359-366.
3. Cima A., Gasull A., Manosas F. Cyclicity of a family of vector fields. J. Math. Anal. Appl. 196:1995;921-937.
4. Han M. Bifurcations of limit cycles and the cusp of order n. Acta Math. Sinica, New Series. 13:1997;64-75.
5. Han M. Cyclicity of planar homoclinic loops and quadratic integrable systems. Science in China (Series A). 12:1997;1247-1258.
6. M. Han, and, J. Chen, On the Number of Limit Cycles in Double Homoclinic Bifurcations, Report Series, CDSNS98-308, Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology.
7. Han M., Wang Z. Differentiability problem of Melnikov functions at a center. J. Syst. Sci. Math. Scis. 17:1997;267-274.
8. Han M., Ye Y., Zhu D. Cyclicity of homoclinic loops and degenerate cubic Hamiltonians. Science in China. 42:1999;605-617.
9. Han M., Zhang Z. Cyclicity 1 and 2 conditions for a 2-polycycle of integrable systems on the plane. J. Differential Equations. 155:1999;245-261.
10. Han M., Zhu D. Bifurcation Theory of Differential Equations. 1994;Coal Industry Publishing House, Beijing.
11. Li B., Zhang Z. A note on a G. S. Petrov's result about the weakened 16th Hilbert problem. J. Math. Anal. Appl. 190:1995;489-516.
12. Lins A., De Melo W., Pugh C. C. On Lienard's equation. Lecture Notes in Mathematics. 1977;Springer-Verlag, New York. p. 335-357.
13. Lloyd N. G., Lynch S. Small-amplitude limit cycles of certain Lienard systems. Proc. Roy. Soc. London Ser. A. 418:1988;199-208.
14. Luo D., Wang X., Zhu D., Han M. Bifurcation Theory and Methods of Dynamical Systems. Advanced Series in Dynamical Systems. 15:1997;World Scientific, Singapore.
15. Mardesic S. The number of limit cycles of polynomial deformations of a Hamiltonian vector field. Erg. Theory Dynam. Syst. 10:1990;523-529.
16. Petrov G. S. The Chebyshev property of elliptic integrals. Funct. Anal. Appl. 22:1988;72-73.
17. Roussarie R. On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields. Bol. Soc. Brasil Mat. 7:1986;67-101.
18. Ye Y. Theory of Limit Cycles. Transl. Math. Monographs. 66:1986;Amer. Math. Soc. Providence.