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Volumn 284, Issue 1, 2003, Pages 236-249

The necessary and sufficient conditions for the existence of periodic orbits in a Lotka-Volterra system

Author keywords

Center manifold theorem for flows; Existence of periodic orbits; Hopf bifurcation; Lotka Volterra model of three species

Indexed keywords


EID: 0042353661     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-247X(03)00340-8     Document Type: Article
Times cited : (11)

References (7)
  • 1
    • 0033239775 scopus 로고    scopus 로고
    • Darboux method and search of invariants for the Lotka-Volterra and complex quadratic systems
    • L. Cairó, M.R. Feix, J. Llibre, Darboux method and search of invariants for the Lotka-Volterra and complex quadratic systems, J. Math. Phys. 40 (1999) 2440-2455.
    • (1999) J. Math. Phys. , vol.40 , pp. 2440-2455
    • Cairó, L.1    Feix, M.R.2    Llibre, J.3
  • 3
    • 0031997312 scopus 로고    scopus 로고
    • On the asymmetric May-Leonard model of three competing species
    • C.-W. Chi, S.-B. Hsu, L.-I. Wu, On the asymmetric May-Leonard model of three competing species, SIAM J. Appl. Math. 58 (1998) 211-226.
    • (1998) SIAM J. Appl. Math. , vol.58 , pp. 211-226
    • Chi, C.-W.1    Hsu, S.-B.2    Wu, L.-I.3
  • 4
    • 0003136372 scopus 로고
    • Mémorie sur les équations différentielles algébriques du premier ordre et du primier degre (mélanges)
    • G. Darboux, Mémorie sur les équations différentielles algébriques du premier ordre et du primier degre (mélanges), Bull. Sci. Math. 60 (1978) 123-144.
    • (1978) Bull. Sci. Math. , vol.60 , pp. 123-144
    • Darboux, G.1
  • 5
    • 84956106116 scopus 로고
    • Systems of differential equations that are competitive or cooperative, III: Competing species
    • M.W. Hirsch, S. Smale, Systems of differential equations that are competitive or cooperative, III: Competing species, Nonlinearity 1 (1988) 51-71.
    • (1988) Nonlinearity , vol.1 , pp. 51-71
    • Hirsch, M.W.1    Smale, S.2
  • 6
    • 0000926545 scopus 로고    scopus 로고
    • On a Lotka-Volterra model which can be projected to a sphere
    • T. Uno, K. Odani, On a Lotka-Volterra model which can be projected to a sphere, Nonlinear Anal. 30 (1997) 1405-1410.
    • (1997) Nonlinear Anal. , vol.30 , pp. 1405-1410
    • Uno, T.1    Odani, K.2
  • 7
    • 0003268664 scopus 로고
    • Qualitative Theory of Differential Equations
    • American Mathematical Society, Providence, RI
    • Z.-F. Zhang, et al., Qualitative Theory of Differential Equations, in: Translations of Mathematical Monographs, Vol. 101, American Mathematical Society, Providence, RI, 1992.
    • (1992) Translation of Mathematical Monographs , vol.101
    • Zhang, Z.-F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.