Bifurcation of limit cycles and integrability of planar dynamical systems in complex form

Journal of Physics A: Mathematical and General

Volumn 32, Issue 10, 1999, Pages 1973-1984

  Lloyd, N G ^a   Pearson, J M ^a  

^a ABERYSTWYTH UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033548331     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/32/10/014     Document Type: Article

References (16)

1. Chavarriga J 1994 Integrable systems in the plane with a centre linear part Appl. Math. 22 285-309
2. Francoise J-P and Pons R 1996 Une approche algorithmique du problème du centre pour des perturbations homogènes Bull. Sci. Math. 120 1-17
3. Gasull A, Guillamon A and Manosa V 1996 An analytical-numerical method of computation of the Liapunov and period constants derived from their algebraic structure Preprint No 6, Universitat Autonoma de Barcelona
4. Kertész V and Kooij R E 1991 Degenerate Hopf bifurcation in two dimensions Nonlinear Anal. 17 267-83
5. Kukles I 1944 Sur les conditions nécessaire et suffisantes pour l'existence d'un centre Dokl. Akad. Nauk 42 160-3
6. Lloyd N G and Pearson J M 1990 REDUCE and the bifurcation of limit cycles J. Symbolic Comput. 9 215-24
7. Lloyd N G and Pearson J M 1990 Conditions for a centre and the bifurcation of limit cycles in a class of cubic systems Bifurcations of Planar Vector Fields ed J-P Francoise and R Roussarie (Berlin: Springer)
8. Lloyd N G and Pearson J M 1992 Computing centre conditions for certain cubic systems J. Comput. Appl. Math. 40 323-36
9. Lloyd N G and Pearson J M 1997 Five limit cycles for a simple cubic system Publ. Math. 41 199-208
10. Lloyd N G, Pearson J M and Romanovsky V G 1996 Computing integrability conditions for a cubic differential system Comput. Math. Appl. 32 99-107
11. Lloyd N G, Pearson J M, Saez E and Szanto I 1996 Limit cycles of a cubic Kolmogorov system Appl. Math. Lett. 9 15-18
12. Pearson J M, Lloyd N G and Christopher C J 1996 Algorithmic derivation of centre conditions SIAM Rev. 38 619-36
13. Romanovsky V G 1995 The centre conditions for the cubic system with four complex parameters Differentsial'nye Uravneniya 31 1091-3
14. Sheplev V S and Bryxina N A and Slin'ko 1998 The algorithm of calculation of Liapunov's coefficients by analysis of chemical self-sustained oscilliations Dokl. Akad. Nauk 359 789-92
15. Shi Song-Ling 1984 On the structure of Poincaré-Liapunov constants for the weak focus of polynomial vector fields J. Diff. Eqns 52 52-7
16. Wang Y and Merino J 1990 Self-organisational origin of agates: banding, fibre twisting, composition and dynamic crystallization model Geochim. Cosmochim. Acta 54 1627-38