On the uniqueness of limit cycles surrounding one or more singularities for Liénard equations

Nonlinearity

Volumn 9, Issue 6, 1996, Pages 1489-1500

  Dumortier, Freddy ^a   Li, Chengzhi ^b  

^a HASSELT UNIVERSITY   (Belgium)

^b PEKING UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001316734     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/9/6/006     Document Type: Article

References (7)

1. Coppel W A 1988 Some quadratic systems with at most one limit cycle Dynamics Reported vol 2 (New York: Wiley) pp 61-8
2. Dumortier F 1993 Techniques in the theory of local bifurcations: blow-up, normal forms, nilpotent bifurcations, singular perturbations Bifurcations and Periodic Orbits of Vector Fields (NATO ASI Series, Series C: Mathematics and Physical Sciences, vol 408) ed D Schlomiuk (NATO) pp 19-73.
3. Dumortier F and Rousseau C 1990 Cubic Liénard equations with linear damping Nonlinearity 3 1015-39
4. Dumortier F and Roussarie R 1991 Tracking limit cycles escaping from rescaling domains Proc. Int. Conf. on Dynamical Systems and Related Topics (Advanced Series in Dynamical Systems vol 9) (Singapore: World Scientific) pp 80-99
5. Dumortier F, Roussarie R and Sotomayor J 1991 Generic three-parameter families of planar vector fields, unfoldings of saddle, focus and elliptic singularities with nilpotent linear parts Bifurcations of Planar Vector Fields (Springer Lecture Notes in Mathematics 1480) (Berlin: Springer) pp 1-164
6. Xiao D 1993 Bifurcations of saddle singularity of codimension 3 of a planar vector field with nilpotent linear part Scientia Sinica (Series A) 23 252-60
7. Žoła̧dek H 1991 Abelian integrals in unfoldings of codimension 3 singular vector fields Bifurcations of Planar Vector Fields (Springer Lecture Notes in Mathematics 1480) (Berlin: Springer) pp 165-224