메뉴 건너뛰기




Volumn 66, Issue 8, 2007, Pages 1707-1721

Limit cycles of cubic polynomial vector fields via the averaging theory

Author keywords

Abelian integral; Averaging method; Bifurcation from a center; Limit cycle

Indexed keywords

BIFURCATION (MATHEMATICS); PERTURBATION TECHNIQUES; THEOREM PROVING; TIME VARYING SYSTEMS; VECTORS;

EID: 33846688339     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2006.02.016     Document Type: Article
Times cited : (55)

References (25)
  • 1
    • 0003318109 scopus 로고
    • Dynamical systems I. Ordinary differential equations
    • Springer, Berlin
    • Arnold V.I., and Ilyashenko Y.S. Dynamical systems I. Ordinary differential equations. Encyclopaedia Math. Sci. vol. 1 (1988), Springer, Berlin
    • (1988) Encyclopaedia Math. Sci. , vol.1
    • Arnold, V.I.1    Ilyashenko, Y.S.2
  • 2
    • 0028497510 scopus 로고
    • Bifurcation of limit cycles from centers and separatrix cycles of planar analytic systems
    • Blows T.R., and Perko L.M. Bifurcation of limit cycles from centers and separatrix cycles of planar analytic systems. SIAM Rev. 36 (1994) 341-376
    • (1994) SIAM Rev. , vol.36 , pp. 341-376
    • Blows, T.R.1    Perko, L.M.2
  • 3
    • 0347753280 scopus 로고    scopus 로고
    • Averaging methods for finding periodic orbits via Brouwer degree
    • Buicǎ A., and Llibre J. Averaging methods for finding periodic orbits via Brouwer degree. Bull. Sci. Math. 128 (2004) 7-22
    • (2004) Bull. Sci. Math. , vol.128 , pp. 7-22
    • Buicǎ, A.1    Llibre, J.2
  • 4
    • 33846672368 scopus 로고    scopus 로고
    • A. Buicǎ, J. Llibre, On the number of limit cycles of a perturbed cubic polynomial differential center, Chaos Solitons Fractals (in press)
  • 6
    • 44949277236 scopus 로고
    • Bifurcation of limit cycles from quadratic isochrones
    • Chicone C., and Jacobs M. Bifurcation of limit cycles from quadratic isochrones. J. Differential Equations 91 (1991) 268-326
    • (1991) J. Differential Equations , vol.91 , pp. 268-326
    • Chicone, C.1    Jacobs, M.2
  • 7
    • 0000763063 scopus 로고    scopus 로고
    • On the nonexistence, existence and uniqueness of limit cycles
    • Giacomini H., Llibre J., and Viano M. On the nonexistence, existence and uniqueness of limit cycles. Nonlinearity 9 (1996) 501-516
    • (1996) Nonlinearity , vol.9 , pp. 501-516
    • Giacomini, H.1    Llibre, J.2    Viano, M.3
  • 8
    • 0034230427 scopus 로고    scopus 로고
    • On the shape of limit cycles that bifurcate from Hamiltonian centers
    • Giacomini H., Llibre J., and Viano M. On the shape of limit cycles that bifurcate from Hamiltonian centers. Nonlinear Anal. 41 (2000) 523-537
    • (2000) Nonlinear Anal. , vol.41 , pp. 523-537
    • Giacomini, H.1    Llibre, J.2    Viano, M.3
  • 9
    • 0035284026 scopus 로고    scopus 로고
    • On the shape of limit cycles that bifurcate from non-Hamiltonian centers
    • Giacomini H., Llibre J., and Viano M. On the shape of limit cycles that bifurcate from non-Hamiltonian centers. Nonlinear Anal. 43 (2001) 837-859
    • (2001) Nonlinear Anal. , vol.43 , pp. 837-859
    • Giacomini, H.1    Llibre, J.2    Viano, M.3
  • 10
    • 0003222562 scopus 로고
    • Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
    • Springer-Verlag, New York
    • Guckenheimer J., and Holmes P. Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Applied Mathematical Sciences vol. 42 (1986), Springer-Verlag, New York
    • (1986) Applied Mathematical Sciences , vol.42
    • Guckenheimer, J.1    Holmes, P.2
  • 11
    • 3242726041 scopus 로고    scopus 로고
    • The number and distributions of limit cycles in a cubic system
    • Han M. The number and distributions of limit cycles in a cubic system. Chinese Ann. Math. Ser. A 23 (2002) 143-152
    • (2002) Chinese Ann. Math. Ser. A , vol.23 , pp. 143-152
    • Han, M.1
  • 12
    • 0001171535 scopus 로고
    • Bifurcations of limit cycles forming compound eyes in the cubic system
    • Li J., and Huang Q.-M. Bifurcations of limit cycles forming compound eyes in the cubic system. Chinese Ann. Math. Ser. B 8 (1987) 391-403
    • (1987) Chinese Ann. Math. Ser. B , vol.8 , pp. 391-403
    • Li, J.1    Huang, Q.-M.2
  • 13
    • 0037052007 scopus 로고    scopus 로고
    • Linear estimation of the number of zeros of abelian integrals for some cubic isochronous centers
    • Li C., Li W., Llibre J., and Zhang Z. Linear estimation of the number of zeros of abelian integrals for some cubic isochronous centers. J. Differential Equations 180 (2002) 307-333
    • (2002) J. Differential Equations , vol.180 , pp. 307-333
    • Li, C.1    Li, W.2    Llibre, J.3    Zhang, Z.4
  • 14
    • 15844417851 scopus 로고    scopus 로고
    • Averaging theory and limit cycles for quadratic systems
    • Llibre J. Averaging theory and limit cycles for quadratic systems. Rad. Mat. 11 (2002/3) 215-228
    • (2002) Rad. Mat. , vol.11 , pp. 215-228
    • Llibre, J.1
  • 16
    • 33846656902 scopus 로고    scopus 로고
    • Global bifurcations of limit cycles for a cubic system
    • Meng Z., Han M., and Gu S. Global bifurcations of limit cycles for a cubic system. Ann. Differential Equations 16 (2000) 263-269
    • (2000) Ann. Differential Equations , vol.16 , pp. 263-269
    • Meng, Z.1    Han, M.2    Gu, S.3
  • 17
    • 0001852349 scopus 로고
    • Über Autoschwingungssysteme, die den hamiltonshen nahe liegen
    • Pontrjagin L.S. Über Autoschwingungssysteme, die den hamiltonshen nahe liegen. Physikalische Zeitschrift der Sowjetunion Band 6, Heft(1-2) (1934) 25-28
    • (1934) Physikalische Zeitschrift der Sowjetunion , vol.6 , Issue.1-2 , pp. 25-28
    • Pontrjagin, L.S.1
  • 18
    • 0003229603 scopus 로고
    • Averaging methods in nonlinear dynamical systems
    • Springer-Verlag, New York
    • Sanders J.A., and Verhulst F. Averaging methods in nonlinear dynamical systems. Applied Mathematical Sci. vol. 59 (1985), Springer-Verlag, New York
    • (1985) Applied Mathematical Sci. , vol.59
    • Sanders, J.A.1    Verhulst, F.2
  • 19
    • 33745158252 scopus 로고    scopus 로고
    • The Poincaré bifurcation of cubic Hamiltonian systems with a global center
    • Song Y. The Poincaré bifurcation of cubic Hamiltonian systems with a global center. Acta Math. Sin. 47 (2004) 291-298
    • (2004) Acta Math. Sin. , vol.47 , pp. 291-298
    • Song, Y.1
  • 21
    • 0036027606 scopus 로고    scopus 로고
    • Arbitrary order bifurcations for perturbed Hamiltonian planar systems via the reciprocal of an integrating factor
    • Viano M., Llibre J., and Giacomini H. Arbitrary order bifurcations for perturbed Hamiltonian planar systems via the reciprocal of an integrating factor. Nonlinear Anal. 48 (2002) 117-136
    • (2002) Nonlinear Anal. , vol.48 , pp. 117-136
    • Viano, M.1    Llibre, J.2    Giacomini, H.3
  • 22
    • 0000564377 scopus 로고    scopus 로고
    • Abelian integrals for cubic vector fields
    • Zhao Y., and Zhang Z. Abelian integrals for cubic vector fields. Ann. Mat. Pura Appl. (4) 176 (1999) 251-272
    • (1999) Ann. Mat. Pura Appl. (4) , vol.176 , pp. 251-272
    • Zhao, Y.1    Zhang, Z.2
  • 23
    • 0001120272 scopus 로고    scopus 로고
    • Bifurcations of limit cycles from cubic Hamiltonian systems with a center and a homoclinic saddle-loop
    • Zhao Y., and Zhang Z. Bifurcations of limit cycles from cubic Hamiltonian systems with a center and a homoclinic saddle-loop. Publ. Mat. 44 (2000) 205-235
    • (2000) Publ. Mat. , vol.44 , pp. 205-235
    • Zhao, Y.1    Zhang, Z.2
  • 24
    • 0000113158 scopus 로고
    • Eleven small limit cycles in a cubic vector field
    • Żoła̧dek H. Eleven small limit cycles in a cubic vector field. Nonlinearity 8 (1995) 843-860
    • (1995) Nonlinearity , vol.8 , pp. 843-860
    • Zoła̧dek, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.