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Volumn 26, Issue 4, 2010, Pages 779-798

Bifurcations of limit cycles in a Z4-equivariant quintic planar vector field

Author keywords

Bifurcation; Compounded cycle; Distribution of limit cycles; Double homoclinic loops; Limit cycles; Stability

Indexed keywords


EID: 77952805362     PISSN: 14398516     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10114-010-6487-2     Document Type: Article
Times cited : (10)

References (27)
  • 1
    • 0037246396 scopus 로고    scopus 로고
    • Hilbert's 16th problem and bifurcations of planar polynomial vector fields
    • Li, J. B.: Hilbert's 16th problem and bifurcations of planar polynomial vector fields. International Journal of Bifurcation and Chaos, 13(1), 47-106 (2003).
    • (2003) International Journal of Bifurcation and Chaos , vol.13 , Issue.1 , pp. 47-106
    • Li, J.B.1
  • 3
    • 0001211762 scopus 로고
    • Bifurcation set and limit cycles forming compound eyes in a perturbed Hamiltonian system
    • Li, J., Liu, Z.: Bifurcation set and limit cycles forming compound eyes in a perturbed Hamiltonian system. Publications Mathematiques, 35, 487-506 (1991).
    • (1991) Publications Mathematiques , vol.35 , pp. 487-506
    • Li, J.1    Liu, Z.2
  • 5
    • 0037246457 scopus 로고    scopus 로고
    • The same distribution of limit cycles in five perturbed cubic Hamiltonian systems
    • Liu, Z., Yang, Z., Jiang, T.: The same distribution of limit cycles in five perturbed cubic Hamiltonian systems. International Journal of Bifurcations and Chaos, 13(1), 243-249 (2003).
    • (2003) International Journal of Bifurcations and Chaos , vol.13 , Issue.1 , pp. 243-249
    • Liu, Z.1    Yang, Z.2    Jiang, T.3
  • 7
    • 24144462859 scopus 로고    scopus 로고
    • Twelve limit cycles in a cubic case of the 16th Hilbert problem
    • Yu, P., Han, M. A.: Twelve limit cycles in a cubic case of the 16th Hilbert problem. Int. J. Bifurcation and Chaos, 15(7), 2191-2205 (2005).
    • (2005) Int. J. Bifurcation and Chaos , vol.15 , Issue.7 , pp. 2191-2205
    • Yu, P.1    Han, M.A.2
  • 8
    • 2942666280 scopus 로고    scopus 로고
    • Bifurcations of limit cycles for a cubic Hamiltonian system under quartic perturbations
    • Zhang, T. H., Han, M. A., Zang, H., et al.: Bifurcations of limit cycles for a cubic Hamiltonian system under quartic perturbations. Chaos, Solitons and Fractals, 22, 1127-1138 (2004).
    • (2004) Chaos, Solitons and Fractals , vol.22 , pp. 1127-1138
    • Zhang, T.H.1    Han, M.A.2    Zang, H.3
  • 9
    • 39449110485 scopus 로고    scopus 로고
    • Bifurcation of limit cycles in a 4-th order near Hamiltonian system
    • Han, M. A., Shang, D. S., Zheng, W., et al.: Bifurcation of limit cycles in a 4-th order near Hamiltonian system. International Journal of Bifurcation and Chaos, 17(11), 4117-4144 (2007).
    • (2007) International Journal of Bifurcation and Chaos , vol.17 , Issue.11 , pp. 4117-4144
    • Han, M.A.1    Shang, D.S.2    Zheng, W.3
  • 13
    • 52649094247 scopus 로고    scopus 로고
    • 6-equivariant planar vector field of degree 5
    • 6-equivariant planar vector field of degree 5. Sci. China Ser. A, 45(7), 817-826 (2002).
    • (2002) Sci. China Ser. A , vol.45 , Issue.7 , pp. 817-826
    • Li, J.1    Chan, H.S.Y.2    Chung, K.W.3
  • 15
    • 52149110343 scopus 로고    scopus 로고
    • On the number and distributions of limit cycles in a quintic planar vector field
    • Wu, Y. H., Gao, Y. X., Han, M. A.: On the number and distributions of limit cycles in a quintic planar vector field. International Journal of Bifurcation and Chaos, 18(7), 1939-1955 (2008).
    • (2008) International Journal of Bifurcation and Chaos , vol.18 , Issue.7 , pp. 1939-1955
    • Wu, Y.H.1    Gao, Y.X.2    Han, M.A.3
  • 16
    • 20444455852 scopus 로고    scopus 로고
    • Bifurcation of limit cycles in a quintic Hamiltonian system under a sixth-order perturbation
    • Wang, S., Yu, P.: Bifurcation of limit cycles in a quintic Hamiltonian system under a sixth-order perturbation. Chaos, Solitons and Fractals, 26, 1317-1335 (2005).
    • (2005) Chaos, Solitons and Fractals , vol.26 , pp. 1317-1335
    • Wang, S.1    Yu, P.2
  • 19
    • 12244310522 scopus 로고    scopus 로고
    • On the stability of double homoclinic loop
    • Han, M. A., Wu, Y. H.: On the stability of double homoclinic loop. Applied Mathematics Letters, 17, 1291-1298 (2004).
    • (2004) Applied Mathematics Letters , vol.17 , pp. 1291-1298
    • Han, M.A.1    Wu, Y.H.2
  • 22
    • 0000495631 scopus 로고
    • On the number of limit cycles which appear with the variation of coeffcients from an equilibrium position of focus or center type
    • Bautin, N. N.: On the number of limit cycles which appear with the variation of coeffcients from an equilibrium position of focus or center type. Mat. Sbornik NS, 30(72), 181-196 (1952).
    • (1952) Mat. Sbornik NS , vol.30 , Issue.72 , pp. 181-196
    • Bautin, N.N.1
  • 23
    • 0033165088 scopus 로고    scopus 로고
    • Cyclicity 1 and 2 conditions for a 2-polycycle of integrable systems on the plane
    • Han, M., Zhang, Z.: Cyclicity 1 and 2 conditions for a 2-polycycle of integrable systems on the plane. J. Diff. Eqns., 155, 245-261 (1999).
    • (1999) J. Diff. Eqns. , vol.155 , pp. 245-261
    • Han, M.1    Zhang, Z.2
  • 24
    • 1942456463 scopus 로고    scopus 로고
    • Bifurcation of limit cycles near polycycles with n vertices
    • Han, M., Wu, Y. H., Ping, B.: Bifurcation of limit cycles near polycycles with n vertices. Chaos, Solitons and Fractals, 22, 383-394 (2004).
    • (2004) Chaos, Solitons and Fractals , vol.22 , pp. 383-394
    • Han, M.1    Wu, Y.H.2    Ping, B.3
  • 25
    • 4944221597 scopus 로고    scopus 로고
    • On the study of bifurcation of the generalize Rayleigh-Liénard oscillator
    • Wu, Y. H., Han, M., Chen, X. F.: On the study of bifurcation of the generalize Rayleigh-Liénard oscillator. International Journal of Bifurcation and Chaos, 14(8), 2905-2914 (2004).
    • (2004) International Journal of Bifurcation and Chaos , vol.14 , Issue.8 , pp. 2905-2914
    • Wu, Y.H.1    Han, M.2    Chen, X.F.3
  • 26
    • 0042689676 scopus 로고    scopus 로고
    • On the number of limit cycles in double homoclinic bifurcations
    • Han, M., Chen, J.: On the number of limit cycles in double homoclinic bifurcations. Science in China, Series A: Mathematics, 43(12), 914-928 (2000).
    • (2000) Science in China, Series A: Mathematics , vol.43 , Issue.12 , pp. 914-928
    • Han, M.1    Chen, J.2
  • 27
    • 0037408724 scopus 로고    scopus 로고
    • On the stability of double homoclinic and heteroclinic cycles
    • Han, M., Hu, S. C., Liu, X. B.: On the stability of double homoclinic and heteroclinic cycles. Nonlinear Analysis, 53, 701-713 (2003).
    • (2003) Nonlinear Analysis , vol.53 , pp. 701-713
    • Han, M.1    Hu, S.C.2    Liu, X.B.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.