메뉴 건너뛰기




Volumn 59, Issue 5, 1999, Pages 1540-1551

On the dynamics of Lotka-Volterra equations having an invariant hyperplane

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTIONS; INTEGRATION; MATHEMATICAL MODELS; POLYNOMIALS; VECTORS;

EID: 0033335405     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139997319463     Document Type: Article
Times cited : (23)

References (24)
  • 5
    • 0007835817 scopus 로고    scopus 로고
    • Bi-Hamiltonian systems and Lotka-Volterra equations: A three-dimensional classification
    • M. PLANK, Bi-Hamiltonian systems and Lotka-Volterra equations: A three-dimensional classification, Nonlinearity, 9 (1996), pp. 887-896.
    • (1996) Nonlinearity , vol.9 , pp. 887-896
    • Plank, M.1
  • 7
    • 0000063856 scopus 로고
    • On the occurrence of limit cycles in the Volterra-Lotka equations
    • J. HOFBAUER, On the occurrence of limit cycles in the Volterra-Lotka equations, J. Nonlinear Anal., 5 (1981), pp. 1003-1007.
    • (1981) J. Nonlinear Anal. , vol.5 , pp. 1003-1007
    • Hofbauer, J.1
  • 8
    • 84912659874 scopus 로고
    • A contribution to the theory of forced oscillations in a generator with two degrees of freedom
    • A. MAYER, A contribution to the theory of forced oscillations in a generator with two degrees of freedom, Tech. Phys. USSR, 3 (1936), pp. 1056-1071.
    • (1936) Tech. Phys. USSR , vol.3 , pp. 1056-1071
    • Mayer, A.1
  • 9
    • 0002562820 scopus 로고
    • Bifurcations of a certain family of planar vector fields tangent to axis
    • H. ZOLADEK, Bifurcations of a certain family of planar vector fields tangent to axis. J. Differential Equations, 67 (1987), pp. 1-55.
    • (1987) J. Differential Equations , vol.67 , pp. 1-55
    • Zoladek, H.1
  • 10
    • 0001251052 scopus 로고
    • Periodic orbits for convex Hamiltonian systems
    • A. WEINSTEIN, Periodic orbits for convex Hamiltonian systems, Ann. Math., 108 (1978), pp. 507-518.
    • (1978) Ann. Math. , vol.108 , pp. 507-518
    • Weinstein, A.1
  • 11
    • 84980196930 scopus 로고
    • Periodic solutions of Hamiltonian systems
    • P. RABINOWITZ, Periodic solutions of Hamiltonian systems, Comm. Pure Appl. Math., 31 (1978), pp. 157-184.
    • (1978) Comm. Pure Appl. Math. , vol.31 , pp. 157-184
    • Rabinowitz, P.1
  • 12
    • 0001569894 scopus 로고
    • Families of invariants of the motion for the Lotka-Volterra equations: The linear polynomials family
    • L. CAIRO AND M. FEIX, Families of invariants of the motion for the Lotka-Volterra equations: The linear polynomials family, J. Math. Phys., 33 (1992), pp. 2440-2455.
    • (1992) J. Math. Phys. , vol.33 , pp. 2440-2455
    • Cairo, L.1    Feix, M.2
  • 13
    • 84972531238 scopus 로고
    • The local structure of Poisson manifolds
    • A. WEINSTEIN, The local structure of Poisson manifolds, J. Differential Geom., 18 (1983), pp. 523-557.
    • (1983) J. Differential Geom. , vol.18 , pp. 523-557
    • Weinstein, A.1
  • 15
    • 21844482825 scopus 로고
    • Hamiltonian structures for the n dimensional Lotka-Volterra equations
    • M. PLANK, Hamiltonian structures for the n dimensional Lotka-Volterra equations, J. Math. Phys., 36 (1995), pp. 3520-3534.
    • (1995) J. Math. Phys. , vol.36 , pp. 3520-3534
    • Plank, M.1
  • 16
    • 0343945601 scopus 로고
    • Geometric, methods in population dynamics
    • X. Liu and D. Siegel, eds., Marcel Dekker, New York
    • M. L. ZEEMAN, Geometric, methods in population dynamics, in Comparison Methods and Stability Theory, X. Liu and D. Siegel, eds., Marcel Dekker, New York, 1994, pp. 339-347.
    • (1994) Comparison Methods and Stability Theory , pp. 339-347
    • Zeeman, M.L.1
  • 18
    • 43949156327 scopus 로고
    • Multiple limit cycles for three dimensional Lotka-Volterra equations
    • J. HOFBAUER AND J. SO, Multiple limit cycles for three dimensional Lotka-Volterra equations, Appl. Math. Lett., 7 (1994), pp. 65-70.
    • (1994) Appl. Math. Lett. , vol.7 , pp. 65-70
    • Hofbauer, J.1    So, J.2
  • 21
    • 0013223658 scopus 로고
    • On periodic solutions necr equilibrium points of conservative systems
    • J. DUISTERMAAT, On periodic solutions necr equilibrium points of conservative systems, Arch. Rational Mech. Anal., 45 (1972), pp. 143-160.
    • (1972) Arch. Rational Mech. Anal. , vol.45 , pp. 143-160
    • Duistermaat, J.1
  • 22
    • 84980140116 scopus 로고
    • Periodic orbits near an equilibrium and a theorem by Alan Weinstein
    • J. MOSER, Periodic orbits near an equilibrium and a theorem by Alan Weinstein, Comm. Pure Appl. Math., 29 (1976), pp. 727-747.
    • (1976) Comm. Pure Appl. Math. , vol.29 , pp. 727-747
    • Moser, J.1
  • 23
    • 0004029931 scopus 로고
    • Dynamical Systems III: Mathematical Aspects of Classical and Celestial Mechanics, 2nd ed
    • Springer-Verlag, Berlin
    • V. ARNOLD, Dynamical Systems III: Mathematical Aspects of Classical and Celestial Mechanics, 2nd ed., Encyclopeadia of Math. Sci. 3, Springer-Verlag, Berlin, 1993.
    • (1993) Encyclopeadia of Math. Sci. , vol.3
    • Arnold, V.1
  • 24
    • 0003460860 scopus 로고
    • Dynamical Systems IV: Symplectic Geometry and Its Applications
    • Springer-Verlag, Berlin
    • V. ARNOLD, Dynamical Systems IV: Symplectic Geometry and Its Applications, Encyclopedia of Math. Sci. 4, Springer-Verlag, Berlin, 1990
    • (1990) Encyclopedia of Math. Sci. , vol.4
    • Arnold, V.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.