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Volumn 21, Issue 2, 2011, Pages 425-429

Four normal size limit cycles in two-dimensional quadratic systems

Author keywords

bifurcation of semistable cycle; instability; Lienard equation; Limit cycle; Lyapunov values; stability; weak focus

Indexed keywords

BIFURCATION (MATHEMATICS); CONVERGENCE OF NUMERICAL METHODS; PLASMA STABILITY;

EID: 79953905237     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127411028532     Document Type: Article
Times cited : (5)

References (9)
  • 1
    • 33847683977 scopus 로고    scopus 로고
    • The geometry of quadratic differential systems with a weak focus of second order
    • DOI 10.1142/S0218127406016720, PII S0218127406016720
    • Artes, J. C. & Llibre, J. [2006] "The geometry of quadratic differential systems with a weak focus of second order," Int. J. Bifurcation and Chaos 16, 3127-3194. (Pubitemid 46357326)
    • (2006) International Journal of Bifurcation and Chaos , vol.16 , Issue.11 , pp. 3127-3194
    • Aktes, J.C.1    Llibre, J.2    Schlomiuk, D.3
  • 2
    • 77955227035 scopus 로고
    • The number of limit cycles appeared under changes of coefficients from a focus or center type equilibrium
    • Bautin, N. N. [1934] "The number of limit cycles appeared under changes of coefficients from a focus or center type equilibrium," Dokl. AN SSSR 24, 668-671.
    • (1934) Dokl. AN SSSR , vol.24 , pp. 668-671
    • Bautin, N.N.1
  • 3
    • 0000255706 scopus 로고
    • On the number of limit cycles which appear with the variation of the coefficients from an equilibrium position of focus or center type
    • Bautin, N. N. [1954] "On the number of limit cycles which appear with the variation of the coefficients from an equilibrium position of focus or center type," Transl. Amer. Math. Soc. 1, 396-413.
    • (1954) Transl. Amer. Math. Soc. , vol.1 , pp. 396-413
    • Bautin, N.N.1
  • 4
    • 10344239862 scopus 로고    scopus 로고
    • Quadratic systems with limit cycles of normal size Buletinul Academici de sciinte Moldova
    • Cherkas, L. A., Artes, J. C. & Llibre, J. [2003] "Quadratic systems with limit cycles of normal size," Buletinul Academici de sciinte Moldova. Matematica 1, 31-46.
    • (2003) Matematica , vol.1 , pp. 31-46
    • Cherkas, L.A.1    Artes, J.C.2    Llibre, J.3
  • 5
    • 45149094783 scopus 로고    scopus 로고
    • Hilberts 16th problem for quadratic systems. New methods based on a transformation to the lienard equation
    • Leonov, G. A. [2008] "Hilberts 16th problem for quadratic systems. New methods based on a transformation to the lienard equation," Int. J. Bifurcation and Chaos 18, 877-884.
    • (2008) Int. J. Bifurcation and Chaos , vol.18 , pp. 877-884
    • Leonov, G.A.1
  • 6
    • 66449106381 scopus 로고    scopus 로고
    • Limit cycles of lienard equation with discontinuous coefficients
    • Leonov, G. A. [2009] "Limit cycles of lienard equation with discontinuous coefficients," Dokl. Phys. 54, 238-241.
    • (2009) Dokl. Phys. , vol.54 , pp. 238-241
    • Leonov, G.A.1
  • 7
    • 77950385744 scopus 로고    scopus 로고
    • Necessary and sufficient conditions for the boundedness of solutions of two-dimensional quadratic systems in positively invariant palf-plane
    • Leonov, G. A. [2010] "Necessary and sufficient conditions for the boundedness of solutions of two-dimensional quadratic systems in positively invariant palf-plane," Dokl. Math. 81, 1-3.
    • (2010) Dokl. Math. , vol.81 , pp. 1-3
    • Leonov, G.A.1
  • 8
    • 0001012446 scopus 로고
    • A concrete example of the existence of four limit cycles for planar quadratic systems
    • Shi, S. [1980] "A concrete example of the existence of four limit cycles for planar quadratic systems," Sci. Sin. 23, 153-158.
    • (1980) Sci. Sin. , vol.23 , pp. 153-158
    • Shi, S.1
  • 9
    • 49049152726 scopus 로고
    • A method of constructing cycles without contact around a weak focus
    • Shi, S. [1981] "A method of constructing cycles without contact around a weak focus," J. Diff. Eqs. 41, 301-312.
    • (1981) J. Diff. Eqs. , vol.41 , pp. 301-312
    • Shi, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.