Generalized quadratic Liénard equations

Applied Mathematics Letters

Volumn 11, Issue 3, 1998, Pages 7-10

  Lynch, S ^a  

^a MANCHESTER METROPOLITAN UNIVERSITY   (United Kingdom)

Author keywords

Conditions for a centre; Focal basis; Li nard equations

Indexed keywords

EID: 0002084265     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-9659(98)00025-1     Document Type: Article

References (15)

1. J.M. Pearson, N.G. Lloyd and C.J. Christopher, Algorithmic derivation of centre conditions, SIAM Review 38 (4), 619-636, (1996).
2. R.E. Kooij and A. Zegeling, Qualitative properties of two-dimensional predator-prey systems, Nonlinear Anal. Theory, Meth. and Appl. 29 (6), 693-715, (1997).
3. X. Zeng, Z.-F. Zhang and S. Gao, On the uniqueness of the limit cycle of the generalized Liénard equation, Bull. Lond. Math. Soc. 26, 213-247, (1994).
4. R.E. Kooij and S.H. Jianhua, A note on 'uniqueness of limit cycles in a Liénard-type system', J. Math. Anal. and Appl. 208 (1), 260-276, (1997).
5. S. Lynch, Limit cycles of generalized Liénard equations, Appl. Math. Lett. 8 (6), 15-17, (1995).
6. th Int. Coll. on Differential Equations, (Edited by D. Bainov), pp. 151-157, VSP, (1996).
7. S. Lynch, Liénard systems and the second part of Hilbert's sixteenth problem, Nonlinear Anal. Theory, Meth. and Appl. 30 (to appear).
8. F. Dumortier and L. Chengzhi, On the uniqueness of limit cycles surrounding one or more singularities for Liénard equations, Nonlinearity 9, 1489-1500, (1996).
9. 2, Differensial'nye Uravneniya 8, 1104-1107, (1972).
10. L.A. Cherkas, Conditions for a Liénard equation to have a centre, Differensial'nye Uravneniya 12, 201-206, (1976).
11. i to have a centre, Differensial'nye Uravneniya 14, 1133-1137, (1978).
12. C.J. Christopher, N.G. Lloyd and J.M. Pearson, On Cherkas's method for centre conditions, Nonlin. World 2, 459-469, (1995).
13. C.J. Christopher and N.G. Lloyd, Small-amplitude limit cycles in polynomial Liénard systems, Nonlinear Differential Equations and Applications (to appear).
14. C.J. Christopher, Small-amplitude limit cycle bifurcations in Liénard systems with quadratic damping or restoring forces, (in preparation).
15. S. Lynch, More results on the bifurcation of limit cycles for systems of Liénard type, J. Egypt. Math. Soc. 2, 75-87, (1994).