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Volumn 176, Issue 1, 2006, Pages 341-358

Bifurcations of limit cycles in a cubic system with cubic perturbations

Author keywords

Hamiltonian system; Heteroclinic loop; Homoclinic loop; Limit cycle

Indexed keywords

BIFURCATION (MATHEMATICS); COMPUTATIONAL METHODS; HAMILTONIANS; THEOREM PROVING;

EID: 33646127359     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2005.09.024     Document Type: Article
Times cited : (4)

References (18)
  • 1
    • 0000495631 scopus 로고
    • On the number of limit cycles which appear with the variation of coefficients from an equilibrium position of focus or center type
    • Bautin N.N. On the number of limit cycles which appear with the variation of coefficients from an equilibrium position of focus or center type. Mat. Sbornik (N.S.) 30 72 (1952) 181-196
    • (1952) Mat. Sbornik (N.S.) , vol.30 , Issue.72 , pp. 181-196
    • Bautin, N.N.1
  • 2
    • 0002383108 scopus 로고    scopus 로고
    • Cyclicity of planar homoclinic loops and quadratic integrable systems
    • Han M. Cyclicity of planar homoclinic loops and quadratic integrable systems. Sci. China, Ser. A 40 12 (1997) 1247-1258
    • (1997) Sci. China, Ser. A , vol.40 , Issue.12 , pp. 1247-1258
    • Han, M.1
  • 3
    • 0034656493 scopus 로고    scopus 로고
    • On the Hopf Cyclicity of plane systems
    • Han M. On the Hopf Cyclicity of plane systems. J. Math. Anal. Appl. 245 (2000) 404-422
    • (2000) J. Math. Anal. Appl. , vol.245 , pp. 404-422
    • Han, M.1
  • 4
    • 0033165088 scopus 로고    scopus 로고
    • Cyclicity 1 and 2 conditions for a 2-polycycle of integrable systems on the plane
    • Han M., and Zhang Z. Cyclicity 1 and 2 conditions for a 2-polycycle of integrable systems on the plane. J. Different. Equat. 155 2 (1999) 245-261
    • (1999) J. Different. Equat. , vol.155 , Issue.2 , pp. 245-261
    • Han, M.1    Zhang, Z.2
  • 5
    • 0042689676 scopus 로고    scopus 로고
    • On the number of limit cycles in double homoclinic bifurcations
    • Han M., and Chen J. On the number of limit cycles in double homoclinic bifurcations. Sci. China, Ser A 43 9 (2000) 914-928
    • (2000) Sci. China, Ser A , vol.43 , Issue.9 , pp. 914-928
    • Han, M.1    Chen, J.2
  • 6
    • 0037408724 scopus 로고    scopus 로고
    • On the stability of double homoclinic and heteroclinic cycles
    • Han M., Hu S., and Liu X. On the stability of double homoclinic and heteroclinic cycles. Nonlinear Anal. 53 (2003) 701-713
    • (2003) Nonlinear Anal. , vol.53 , pp. 701-713
    • Han, M.1    Hu, S.2    Liu, X.3
  • 7
    • 0001209273 scopus 로고    scopus 로고
    • Cyclicity of homoclinic loops and degenerate cubic Hamiltonians
    • Han M., Ye Y., and Zhu D. Cyclicity of homoclinic loops and degenerate cubic Hamiltonians. Sci. China, Ser A 42 6 (1999) 605-617
    • (1999) Sci. China, Ser A , vol.42 , Issue.6 , pp. 605-617
    • Han, M.1    Ye, Y.2    Zhu, D.3
  • 8
    • 14844304659 scopus 로고    scopus 로고
    • On the number and distributions of limit cycles in a cubic system
    • Han M., Zhang T., and Zang H. On the number and distributions of limit cycles in a cubic system. Int. J. Bifur. Chaos 14 12 (2004)
    • (2004) Int. J. Bifur. Chaos , vol.14 , Issue.12
    • Han, M.1    Zhang, T.2    Zang, H.3
  • 9
    • 0037246396 scopus 로고    scopus 로고
    • Hilbert's 16th problem and bifurcations of planar polynomial vector fields
    • Li J. Hilbert's 16th problem and bifurcations of planar polynomial vector fields. Int. J. Bifurcat. Chaos 13 1 (2003) 47-106
    • (2003) Int. J. Bifurcat. Chaos , vol.13 , Issue.1 , pp. 47-106
    • Li, J.1
  • 10
    • 0001171535 scopus 로고
    • Bifurcations of limit cycles forming compound eyes in the cubic system
    • Li J., and Huang Q. Bifurcations of limit cycles forming compound eyes in the cubic system. Chin. Ann. Math. 8 4 (1987) 391-403
    • (1987) Chin. Ann. Math. , vol.8 , Issue.4 , pp. 391-403
    • Li, J.1    Huang, Q.2
  • 11
    • 0001211762 scopus 로고
    • Bifurcation set and limit cycles forming compound eyes in a perturbed Hamiltonian system
    • Li J., and Liu Z. Bifurcation set and limit cycles forming compound eyes in a perturbed Hamiltonian system. Publ. Math. 35 (1991) 487-506
    • (1991) Publ. Math. , vol.35 , pp. 487-506
    • Li, J.1    Liu, Z.2
  • 12
    • 0037246457 scopus 로고    scopus 로고
    • The same distribution of limit cycles in five perturbed cubic Hamiltonian systems
    • Liu Z., Yang Z., and Jiang T. The same distribution of limit cycles in five perturbed cubic Hamiltonian systems. Int. J. Bifurcat. Chaos 13 1 (2003) 243-249
    • (2003) Int. J. Bifurcat. Chaos , vol.13 , Issue.1 , pp. 243-249
    • Liu, Z.1    Yang, Z.2    Jiang, T.3
  • 13
    • 51249171477 scopus 로고
    • On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields
    • Roussarie R. On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields. Bol. Soc. Bras. Mat. 17 (1986) 67-101
    • (1986) Bol. Soc. Bras. Mat. , vol.17 , pp. 67-101
    • Roussarie, R.1
  • 14
    • 33646145221 scopus 로고
    • Ame. Math. Soc., Boston
    • Ye Y. Theory of Limit Cycles. Trans. Math. Monographs vol. 66 (1986), Ame. Math. Soc., Boston
    • (1986) Trans. Math. Monographs , vol.66
    • Ye, Y.1
  • 16
    • 0242365778 scopus 로고    scopus 로고
    • Bifurcations of limit cycles in a cubic system
    • Zhang T., Zang H., and Han M. Bifurcations of limit cycles in a cubic system. Chaos Soliton Fract 20 (2004) 629-638
    • (2004) Chaos Soliton Fract , vol.20 , pp. 629-638
    • Zhang, T.1    Zang, H.2    Han, M.3
  • 17
    • 2942666280 scopus 로고    scopus 로고
    • Bifurcations of limit cycles for a cubic Hamiltonian system under quartic perturbations
    • Zhang T., Han M., Hong Z., and Meng X. Bifurcations of limit cycles for a cubic Hamiltonian system under quartic perturbations. Chaos Soliton Fract 22 (2004) 1127-1138
    • (2004) Chaos Soliton Fract , vol.22 , pp. 1127-1138
    • Zhang, T.1    Han, M.2    Hong, Z.3    Meng, X.4
  • 18
    • 3242699921 scopus 로고    scopus 로고
    • Bifurcations of limit cycles from quintic Hamiltonian systems with a double figure eight loop
    • Hong Z., Zhang T., and Chen W. Bifurcations of limit cycles from quintic Hamiltonian systems with a double figure eight loop. J. Complex. 20 4 (2004) 544-560
    • (2004) J. Complex. , vol.20 , Issue.4 , pp. 544-560
    • Hong, Z.1    Zhang, T.2    Chen, W.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.