메뉴 건너뛰기




Volumn 40, Issue 12, 1997, Pages 1247-1258

Cyclicity of planar homoclinic loops and quadratic integrable systems

Author keywords

Bifurcation; Cyclicity; Homoclinic loop; Limit cycle

Indexed keywords


EID: 0002383108     PISSN: 10069283     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02876370     Document Type: Article
Times cited : (60)

References (15)
  • 1
    • 0012818307 scopus 로고
    • Stability of homoclinic loops and bifurcation conditions of limit cycles
    • Feng, B., Qian, M., Stability of homoclinic loops and bifurcation conditions of limit cycles, Acta Math. Sinica, 1985, 28 (1):53.
    • (1985) Acta Math. Sinica , vol.28 , Issue.1 , pp. 53
    • Feng, B.1    Qian, M.2
  • 3
    • 0013455971 scopus 로고
    • On the number of limit cycles bifurcated from a homoclinic or heteroclinic loop
    • Han, M., On the number of limit cycles bifurcated from a homoclinic or heteroclinic loop, Science in China, Series A, 1993, 23(2):113.
    • (1993) Science in China, Series A , vol.23 , Issue.2 , pp. 113
    • Han, M.1
  • 4
    • 51249171477 scopus 로고
    • On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields
    • Rousarie, R., On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields, Bol. Soc. Brasil Mat., 1986, 17:67.
    • (1986) Bol. Soc. Brasil Mat. , vol.17 , pp. 67
    • Rousarie, R.1
  • 6
    • 0000881510 scopus 로고
    • High order Melnikov functions and the problem of uniformity in global bifurcations
    • Zhang, Z., Li, B., High order Melnikov functions and the problem of uniformity in global bifurcations, Annali di Mat. Pura ed Appl. (IV), 1992, Vol. CLXT:181-212.
    • (1992) Annali di Mat. Pura Ed Appl. (IV) , vol.CLXT , pp. 181-212
    • Zhang, Z.1    Li, B.2
  • 7
    • 0010949128 scopus 로고
    • Bifurcations of invariant tori and subharmonic solutions of periodic perturbed systems
    • Han, M., Bifurcations of invariant tori and subharmonic solutions of periodic perturbed systems, Science in China, Series A, 1994, 37(11):1152.
    • (1994) Science in China, Series A , vol.37 , Issue.11 , pp. 1152
    • Han, M.1
  • 8
    • 0002714708 scopus 로고
    • Saddle quantities and applications
    • Joyal, P., Rousseau, C., Saddle quantities and applications, J. Diff. Eqs., 1989, 78:374.
    • (1989) J. Diff. Eqs. , vol.78 , pp. 374
    • Joyal, P.1    Rousseau, C.2
  • 9
    • 0347490017 scopus 로고
    • Saddle values and limit cycles generated by separatrix of quadratic systems
    • (eds. Li Z, Shum K., Yang, C. Le Y.), Singapore: World Scientific
    • Cai, S., Guo, G., Saddle values and limit cycles generated by separatrix of quadratic systems, in Proceedings of Asian Math. Conference '90 (eds. Li Z, Shum K., Yang, C. Le Y.), Singapore: World Scientific, 1992, 25-31.
    • (1992) Proceedings of Asian Math. Conference '90 , pp. 25-31
    • Cai, S.1    Guo, G.2
  • 10
    • 0348120136 scopus 로고
    • A general property of the quadratic differential systems
    • Zhu, D., A general property of the quadratic differential systems, Chin. Ann. Math., 1989, 10B: 26.
    • (1989) Chin. Ann. Math. , vol.10 B , pp. 26
    • Zhu, D.1
  • 11
    • 0346229030 scopus 로고
    • Example of a quadratic system with two cycles appearing in a homoclinic loop bifurcation
    • Rousseau, C., Example of a quadratic system with two cycles appearing in a homoclinic loop bifurcation, J. Diff. Eqs., 1987, 66:140.
    • (1987) J. Diff. Eqs. , vol.66 , pp. 140
    • Rousseau, C.1
  • 13
    • 0038884337 scopus 로고
    • On saddle-loop bifurcations of limit cycles in perturbations of quadratic Hamiltonian systems
    • Horozov, E., Iliev, I., On saddle-loop bifurcations of limit cycles in perturbations of quadratic Hamiltonian systems, J. Diff. Equs., 1994, 113:84.
    • (1994) J. Diff. Equs. , vol.113 , pp. 84
    • Horozov, E.1    Iliev, I.2
  • 14
    • 0001722685 scopus 로고    scopus 로고
    • Higher-order Melnikov functions for degenerate cubic Hamiltonians
    • Iliev, I., Higher-order Melnikov functions for degenerate cubic Hamiltonians, Adv. in Diff. Eqs., 1(4):689.
    • Adv. in Diff. Eqs. , vol.1 , Issue.4 , pp. 689
    • Iliev, I.1
  • 15
    • 0002911460 scopus 로고
    • Bifurcation of limit cycles from quadratic centers
    • Shafer, D., Zegeling, A., Bifurcation of limit cycles from quadratic centers, J. Diff. Eqs., 1995, 122:48.
    • (1995) J. Diff. Eqs. , vol.122 , pp. 48
    • Shafer, D.1    Zegeling, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.