A numerical approach to bifurcations from quadratic centers

Journal of Mathematical Analysis and Applications

Volumn 202, Issue 1, 1996, Pages 90-107

  Shafer, Douglas S ^a   Wu, Xiaonan ^a   Zegeling, André ^a  

^a UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030586580     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1996.0304     Document Type: Article

References (10)

1. 1. E. A. Andronova, Quadratic systems that are close to conservative with four limit cycles, in "Methods of the Qualitative Theory of Differential Equations," pp. 118-126, 166-167, Gorki, 1983.
2. 2. N. N. Bautin, On the number of limit cycles which appear with the variation of the coefficients from an equilibrium point of focus or center type, Mat. Sb. (N.S.) 70 (1952), 181-196 [in Russian]; Amer. Math. Soc. Transl. (1) 5 (1962), 396-413 [Engl. transl.].
3. 2. N. N. Bautin, On the number of limit cycles which appear with the variation of the coefficients from an equilibrium point of focus or center type, Mat. Sb. (N.S.) 70 (1952), 181-196 [in Russian]; Amer. Math. Soc. Transl. (1) 5 (1962), 396-413 [Engl. transl.].
4. 3. W. A. Coppel, Some quadratic systems with at most one limit cycle, Dynamics Report. Ser. Dynam. Syst. Appl. 2 (1988), 61-88.
5. 4. D. Hilbert, Mathematical problems, Bull. Amer. Math. Soc. 8 (1902), 437-479.
6. 5. Yu. S. Il'yashenko, "Finiteness Theorems for Limit Cycles," Translations of Mathematical Monographs, Vol. 94, Amer. Math. Soc., Providence, RI, 1991.
7. 6. D. S. Shafer and A. Zegeling, Bifurcation of limit cycles from quadratic centers, J. Differential Equations 122 (1995) 48-70.
8. 7. S.-L. Shi, On limit cycles of plane quadratic systems, Sci. Sinica 24 (1981), 153-159.
9. 8. A. Zegeling, Perturbations of non-Hamiltonian centers in quadratic centers, preprint, 1993.
10. 9. H. Zolładek, Quadratic systems with a center and their perturbations, J. Differential Equations 109 (1994), 223-273.