메뉴 건너뛰기




Volumn 33, Issue 12, 2000, Pages 2395-2406

Darboux integrability for 3D Lotka-Volterra systems

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0034737212     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/33/12/307     Document Type: Article
Times cited : (58)

References (35)
  • 1
    • 0041020915 scopus 로고
    • Branching of solutions and nonexistence of first integrals in Hamiltonian mechanics I
    • Ziglin S L 1983 Branching of solutions and nonexistence of first integrals in Hamiltonian mechanics I Func. Anal. Appl. 16 181 Ziglin S L 1983 Branching of solutions and nonexistence of first integrals in Hamiltonian mechanics II Func. Anal. Appl. 17 6
    • (1983) Func. Anal. Appl. , vol.16 , pp. 181
    • Ziglin, S.L.1
  • 2
    • 14344258193 scopus 로고
    • Branching of solutions and nonexistence of first integrals in Hamiltonian mechanics II
    • Ziglin S L 1983 Branching of solutions and nonexistence of first integrals in Hamiltonian mechanics I Func. Anal. Appl. 16 181 Ziglin S L 1983 Branching of solutions and nonexistence of first integrals in Hamiltonian mechanics II Func. Anal. Appl. 17 6
    • (1983) Func. Anal. Appl. , vol.17 , pp. 6
    • Ziglin, S.L.1
  • 3
    • 0001875730 scopus 로고
    • A criterion for the nonexistence of an additional integral in Hamiltonian systems with a homogeneous potential
    • Yoshida H 1987 A criterion for the nonexistence of an additional integral in Hamiltonian systems with a homogeneous potential Physica D 29128
    • (1987) Physica D , vol.29 , pp. 128
    • Yoshida, H.1
  • 4
    • 0001003724 scopus 로고
    • Generalizations of Noether's theorem in classical mechanics
    • Cantrijn F and Sarlet W 1981 Generalizations of Noether's theorem in classical mechanics SIAM Rev. 23 467
    • (1981) SIAM Rev. , vol.23 , pp. 467
    • Cantrijn, F.1    Sarlet, W.2
  • 5
    • 0003136372 scopus 로고
    • Mémoire sur les équations différentielles algébriques du premier ordre et du premier degré Mélanges
    • Darboux G 1878 Mémoire sur les équations différentielles algébriques du premier ordre et du premier degré Mélanges Bull. Sci. Math. series 2 2 60, 123, 151
    • (1878) Bull. Sci. Math. Series 2 2 60 , vol.123 , pp. 151
    • Darboux, G.1
  • 7
    • 0040626648 scopus 로고
    • On the complete and partial integrability of non-Hamiltonian systems
    • Bountis T, Grammaticos B and Ramani A 1989 On the complete and partial integrability of non-Hamiltonian systems Phys. Rep. 180 159
    • (1989) Phys. Rep. , vol.180 , pp. 159
    • Bountis, T.1    Grammaticos, B.2    Ramani, A.3
  • 8
    • 84981754671 scopus 로고
    • Integrals of nonlinear equations of evolution and solitary waves
    • Lax P D 1968 Integrals of nonlinear equations of evolution and solitary waves Commun. Pure Appl. Math. 21 467
    • (1968) Commun. Pure Appl. Math. , vol.21 , pp. 467
    • Lax, P.D.1
  • 9
    • 0040215985 scopus 로고
    • Direct methods for the search of the second invariant
    • Hietarinta J 1987 Direct methods for the search of the second invariant Phys. Rep. 147 8
    • (1987) Phys. Rep. , vol.147 , pp. 8
    • Hietarinta, J.1
  • 10
    • 0000983537 scopus 로고
    • A method of finding integrals for three-dimensional dynamical systems
    • Strelcyn J M and Wojciechowski S 1988 A method of finding integrals for three-dimensional dynamical systems Phys. Lett. A 133 207
    • (1988) Phys. Lett. A , vol.133 , pp. 207
    • Strelcyn, J.M.1    Wojciechowski, S.2
  • 11
    • 51249194831 scopus 로고
    • Application de la théorie des équations intégrales linéaires aux systémes d'équations différentielles non linéaires
    • Carleman T 1932 Application de la théorie des équations intégrales linéaires aux systémes d'équations différentielles non linéaires Acta Math. 59 63
    • (1932) Acta Math. , vol.59 , pp. 63
    • Carleman, T.1
  • 12
    • 0013453444 scopus 로고
    • The Lorenz model and the method of Carleman embedding
    • Andrade R F S and Rauh A 1981 The Lorenz model and the method of Carleman embedding Phys. Lett. A 82 276
    • (1981) Phys. Lett. A , vol.82 , pp. 276
    • Andrade, R.F.S.1    Rauh, A.2
  • 13
    • 0000124854 scopus 로고
    • Universal canonical forms for time-continuous dynamical systems
    • Brenig L and Goriely A 1989 Universal canonical forms for time-continuous dynamical systems Phys. Rev. A 40 4119
    • (1989) Phys. Rev. A , vol.40 , pp. 4119
    • Brenig, L.1    Goriely, A.2
  • 14
    • 85032069709 scopus 로고
    • Invariant algebraic curves and conditions for a center
    • Christopher C J 1994 Invariant algebraic curves and conditions for a center Proc. R. Soc. Edin. A 124 1209
    • (1994) Proc. R. Soc. Edin. A , vol.124 , pp. 1209
    • Christopher, C.J.1
  • 15
    • 0002792963 scopus 로고    scopus 로고
    • Algebraic aspects of integrability for polynomial systems
    • Christopher C J and Llibre J 1999 Algebraic aspects of integrability for polynomial systems Qualit. Theory Dynam. Syst. 1 71-95
    • (1999) Qualit. Theory Dynam. Syst. , vol.1 , pp. 71-95
    • Christopher, C.J.1    Llibre, J.2
  • 16
    • 0001211523 scopus 로고    scopus 로고
    • Algebraic solutions for polynomial vector fields with emphasis in the quadratic case
    • Chavarriga J, Llibre J and Sotomayor J 1997 Algebraic solutions for polynomial vector fields with emphasis in the quadratic case Expositiones Math. 15 161
    • (1997) Expositiones Math. , vol.15 , pp. 161
    • Chavarriga, J.1    Llibre, J.2    Sotomayor, J.3
  • 17
    • 0000977295 scopus 로고
    • Computing closed-form solutions of first-order ODEs using the Prelle-Singer procedure
    • Man Yu 1993 Computing closed-form solutions of first-order ODEs using the Prelle-Singer procedure J. Symb. Comput. 16 423
    • (1993) J. Symb. Comput. , vol.16 , pp. 423
    • Man, Yu.1
  • 18
    • 0000313420 scopus 로고
    • Elementary first integrals and algebraic invariant curves of differential equations
    • Schlomiuk D 1993 Elementary first integrals and algebraic invariant curves of differential equations Expositiones Math. 11 433
    • (1993) Expositiones Math. , vol.11 , pp. 433
    • Schlomiuk, D.1
  • 20
    • 0033239775 scopus 로고    scopus 로고
    • Darboux method and search of invariants for the Lotka-Volterra and complex quadratic systems
    • Cairó L, Feix M R and Llibre J 1999 Darboux method and search of invariants for the Lotka-Volterra and complex quadratic systems J. Math. Phys. 40 2074-91
    • (1999) J. Math. Phys. , vol.40 , pp. 2074-2091
    • Cairó, L.1    Feix, M.R.2    Llibre, J.3
  • 21
    • 0012113127 scopus 로고    scopus 로고
    • Integrability and algebraic solutions for planar polynomial differential systems with emphasis on the quadratic systems
    • Cairó L, Feix M R and Llibre J 1999 Integrability and algebraic solutions for planar polynomial differential systems with emphasis on the quadratic systems IME-U5P Resenhas 4 127-61
    • (1999) IME-U5P Resenhas , vol.4 , pp. 127-161
    • Cairó, L.1    Feix, M.R.2    Llibre, J.3
  • 23
    • 0001620238 scopus 로고
    • Analytical note on certain rhythmic relations in organic systems
    • Lotka A J 1920 Analytical note on certain rhythmic relations in organic systems Proc. Natl Acad. Sci. 6 410
    • (1920) Proc. Natl Acad. Sci. , vol.6 , pp. 410
    • Lotka, A.J.1
  • 24
    • 21844500150 scopus 로고
    • Lie symmetries and invariants of the Lotka-Volterra system
    • Almeida M A, Magalhães M E and Moreira I C 1995 Lie symmetries and invariants of the Lotka-Volterra system J. Math. Phys. 36 1854
    • (1995) J. Math. Phys. , vol.36 , pp. 1854
    • Almeida, M.A.1    Magalhães, M.E.2    Moreira, I.C.3
  • 26
    • 0040072253 scopus 로고
    • Invariants for models of interacting populations
    • Cairó L, Feix M R and Goedert J 1989 Invariants for models of interacting populations Phys. Lett. A 140 421
    • (1989) Phys. Lett. A , vol.140 , pp. 421
    • Cairó, L.1    Feix, M.R.2    Goedert, J.3
  • 27
    • 0001569894 scopus 로고
    • Families of invariants of the motion for the Lotka-Volterra equations: The linear polynomials family
    • Cairó L and Feix M R 1992 Families of invariants of the motion for the Lotka-Volterra equations: the linear polynomials family J. Math. Phys. 33 2440
    • (1992) J. Math. Phys. , vol.33 , pp. 2440
    • Cairó, L.1    Feix, M.R.2
  • 28
    • 0030487558 scopus 로고    scopus 로고
    • On the polynomial first integrals of the (a, b, c) Lotka-Volterra system
    • Labrunie S 1996 On the polynomial first integrals of the (a, b, c) Lotka-Volterra system J. Math. Phys. 37 5539
    • (1996) J. Math. Phys. , vol.37 , pp. 5539
    • Labrunie, S.1
  • 29
    • 0001693497 scopus 로고    scopus 로고
    • Polynomial first integrals of the Lotka-Volterra system
    • Moulin-Ollagnier J 1997 Polynomial first integrals of the Lotka-Volterra system Bull. Sci. Math. 121 463
    • (1997) Bull. Sci. Math. , vol.121 , pp. 463
    • Moulin-Ollagnier, J.1
  • 30
    • 0039031906 scopus 로고    scopus 로고
    • Darboux integrability and invariant hyperplanes for d-dimensional polynomial differential systems
    • at press
    • Llibre J and Rodríguez G 2000 Darboux integrability and invariant hyperplanes for d-dimensional polynomial differential systems Bull. Sci. Math. at press
    • (2000) Bull. Sci. Math.
    • Llibre, J.1    Rodríguez, G.2
  • 33
    • 1542795332 scopus 로고
    • Elementary first integrals of differential equations
    • Prelle M J and Singer M F 1983 Elementary first integrals of differential equations Trans. Am. Math. Soc. 279 215
    • (1983) Trans. Am. Math. Soc. , vol.279 , pp. 215
    • Prelle, M.J.1    Singer, M.F.2
  • 34
    • 84968484573 scopus 로고
    • Liouvillian first integrals of differential equations
    • Singer M F 1992 Liouvillian first integrals of differential equations Trans. Am. Math. Soc. 333 673
    • (1992) Trans. Am. Math. Soc. , vol.333 , pp. 673
    • Singer, M.F.1
  • 35
    • 0033209543 scopus 로고    scopus 로고
    • Rational integration of the Lotka-Volterra system
    • Moulin-Ollagnier J 1999 Rational integration of the Lotka-Volterra system Bull. Sci. Math. 123 437
    • (1999) Bull. Sci. Math. , vol.123 , pp. 437
    • Moulin-Ollagnier, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.