A cubic system with eight small-amplitude limit cycles

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

Volumn 47, Issue 2, 1991, Pages 163-171

  James, E M ^a   Lloyd, N G ^a  

^a ABERYSTWYTH UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL TECHNIQUES - DIFFERENTIAL EQUATIONS;

BIFURCATION; CUBIC SYSTEMS; LIMIT CYCLES;

MATHEMATICAL TECHNIQUES;

EID: 0026390187     PISSN: 02724960     EISSN: None     Source Type: Journal    
DOI: 10.1093/imamat/47.2.163     Document Type: Article

References (17)

1. J. M. Abdulrahman 1989 Bifurcation of limit cycles of some polynomial systems. Ph.D. thesis, University College of Wales, Aberystwyth.
2. N. N. Bautin 1952 On the number of limit cycles which appear with the variation of coefficients from an equilibrium position of focus or centre type. Mat. Sb. 30, 181-96 [in Russian]; 1954 Am. Math. Soc. Transl., No. 100.
3. C. J. Christopher & N. G. Lloyd 1990 On the paper of Jin and Wang concerning the conditions for a centre in certain cubic systems. Bull. Lond. Math. Soc. 22, 5-12.
4. E. M. James & N. Yasmin 1989 Limit cycles of a cubic system. Preprint, University College of Wales, Aberystwyth.
5. D. Hilbert 1902 Mathematical problems. Bull. Am. Math. Soc. 8, 437-79.
6. Li Jibin & Bai Jinxin 1989 The cyclicity of multiple Hopf bifurcation in planar cubic differential systems: M(3) 5= 7. Preprint, Kunming Institute of Technology.
7. N. G. Lloyd 1988 Limit cycles of polynomial systems. In: New Directions in dynamical Systems, London Mathematical Society, Lecture Notes Series No. 127 (T. Bedford & J. Swift, eds.). Cambridge University Press, pp. 192-234.
8. N. G. Lloyd 1988 The number of limit cycles of polynomial systems in the plane. Bull. Inst. Math. Applic. 24, 161-5.
9. N. G. Lloyd & T. R. Blows 1984 The number of limit cycles of certain polynomial differential equations. Proc. R. Soc. Edinb. Sect. A 98, 215-39.
10. N. G. Lloyd, T. R. Blows, & M. C. Kalenge 1988 Some cubic systems with several limit cycles. Nonlinearity 1, 653-69.
11. N. G. Lloyd & S. Lynch 1988 Small amplitude limit cycles of certain Li6nard systems. Proc. R. Soc. Lond. Ser. A 418, 199-208.
12. N. G. Lloyd & J. M. Pearson 1990 REDUCE and the bifurcation of limit cycles. /. Symbolic Comput. 9, 215-24.
13. N. G. Lloyd & J. M. Pearson 1990 Computing centre conditions for certain cubic systems. Preprint No. 772, Institute for Mathematics and its Applications, University of Minnesota.
14. V. V. Nemytskii & V. V. Stepanov 1960 Qualitative Theory of Differential Equations. Princeton University Press.
15. J. M. Pearson 1989 Automatic location of roots of polynomials. Internal report, University College of Wales, Aberystwyth.
16. B. L. van der Waerden 1949 Modem Algebra, Vol. 1 [English translation]. New York: Frederick Ungar.
17. Wang Dongmin 1990 A class of cubic differential systems with 6-tuple focus. /. Diff. Eqn. 87, 305-15.