메뉴 건너뛰기




Volumn 16, Issue 3, 2003, Pages 785-801

The dynamical behaviour of type-K competitive Kolmogorov systems and its application to three-dimensional type-K competitive Lotka-Volterra systems

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0242371799     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/16/3/301     Document Type: Article
Times cited : (31)

References (40)
  • 1
    • 0017256150 scopus 로고
    • On the differential equations species in competition
    • Smale S 1976 On the differential equations species in competition J. Math. Biol. 3 5-7
    • (1976) J. Math. Biol. , vol.3 , pp. 5-7
    • Smale, S.1
  • 2
    • 0000885375 scopus 로고
    • Systems of differential equations which are competitive or cooperative I: Limit sets
    • Hirsch M 1982 Systems of differential equations which are competitive or cooperative I: Limit sets SIAM J. Math. Anal. 13 167-79
    • (1982) SIAM J. Math. Anal. , vol.13 , pp. 167-179
    • Hirsch, M.1
  • 3
    • 0001176145 scopus 로고
    • Systems of differential equations which are competitive or cooperative II: Convergence almost everywhere
    • Hirsch M 1985 Systems of differential equations which are competitive or cooperative II: Convergence almost everywhere SIAM J. Math. Anal. 16 423-39
    • (1985) SIAM J. Math. Anal. , vol.16 , pp. 423-439
    • Hirsch, M.1
  • 4
    • 84956106116 scopus 로고
    • Systems of differential equations which are competitive or cooperative III: Competing species
    • Hirsch M 1988 Systems of differential equations which are competitive or cooperative III: Competing species Nonlinearity 1 51-71
    • (1988) Nonlinearity , vol.1 , pp. 51-71
    • Hirsch, M.1
  • 5
    • 0000743387 scopus 로고
    • Competing subcommunities of mutualists and a generalized Kamke theorem
    • Smith H L 1986 Competing subcommunities of mutualists and a generalized Kamke theorem SIAM J. Appl. Math. 46 856-74
    • (1986) SIAM J. Appl. Math. , vol.46 , pp. 856-874
    • Smith, H.L.1
  • 6
    • 21444453892 scopus 로고    scopus 로고
    • Competitive exclusion and coexistence for competitive systems on ordered Banach spaces
    • Hsu S B, Smith H L and Waltman P 1996 Competitive exclusion and coexistence for competitive systems on ordered Banach spaces Trans. Am. Math. Soc. 348 4083-94
    • (1996) Trans. Am. Math. Soc. , vol.348 , pp. 4083-4094
    • Hsu, S.B.1    Smith, H.L.2    Waltman, P.3
  • 7
    • 0035841057 scopus 로고    scopus 로고
    • Stable coexistence and bi-stability for competitive systems on ordered Banach spaces
    • Smith H L and Thieme H R 2001 Stable coexistence and bi-stability for competitive systems on ordered Banach spaces J. Diff. Eqns 176 195-222
    • (2001) J. Diff. Eqns , vol.176 , pp. 195-222
    • Smith, H.L.1    Thieme, H.R.2
  • 8
    • 22844454645 scopus 로고    scopus 로고
    • The necessary and sufficient conditions for the global stability of type-K Lotka-Volterra systems
    • Tu C F and Jiang J F 1999 The necessary and sufficient conditions for the global stability of type-K Lotka-Volterra systems Proc. Am. Math. Soc. 127 3181-6
    • (1999) Proc. Am. Math. Soc. , vol.127 , pp. 3181-3186
    • Tu, C.F.1    Jiang, J.F.2
  • 9
    • 0001018945 scopus 로고    scopus 로고
    • The coexistence of a community of species with limited competition
    • Tu C F and Jiang J F 1998 The coexistence of a community of species with limited competition J. Math. Anal. Appl. 217 553-71
    • (1998) J. Math. Anal. Appl. , vol.217 , pp. 553-571
    • Tu, C.F.1    Jiang, J.F.2
  • 10
    • 0032623132 scopus 로고    scopus 로고
    • Global stability and permanence for a class of type-K monotone systems
    • Tu C F and Jiang J F 1999 Global stability and permanence for a class of type-K monotone systems SIAM J. Math. Anal. 30 360-78
    • (1999) SIAM J. Math. Anal. , vol.30 , pp. 360-378
    • Tu, C.F.1    Jiang, J.F.2
  • 11
    • 0036721857 scopus 로고    scopus 로고
    • On the finite dimensional dynamical systems with limited competition
    • Liang X and Jiang J 2002 On the finite dimensional dynamical systems with limited competition Trans. Am. Math. Soc. 354 3535-54
    • (2002) Trans. Am. Math. Soc. , vol.354 , pp. 3535-3554
    • Liang, X.1    Jiang, J.2
  • 12
    • 0036833148 scopus 로고    scopus 로고
    • The classification of the dynamical behavior of 3-dimensional type-K monotone Lotka-Volterra systems
    • Liang X and Jiang J 2002 The classification of the dynamical behavior of 3-dimensional type-K monotone Lotka-Volterra systems Nonlinear Anal. Ser. A: Theory Methods 51 749-63
    • (2002) Nonlinear Anal. Ser. A: Theory Methods , vol.51 , pp. 749-763
    • Liang, X.1    Jiang, J.2
  • 13
    • 0037457045 scopus 로고    scopus 로고
    • Discrete infinite dimensional type-K monotone dynamical systems and time periodic reaction-diffusion systems
    • at press
    • Liang X and Jiang J 2003 Discrete infinite dimensional type-K monotone dynamical systems and time periodic reaction-diffusion systems J. Diff. Eqns at press
    • (2003) J. Diff. Eqns
    • Liang, X.1    Jiang, J.2
  • 15
    • 0002460864 scopus 로고
    • Analysis of three-species models of mutualism in predator-prey and competitive systems
    • Rai B, Freedman H I and Addicott J F 1983 Analysis of three-species models of mutualism in predator-prey and competitive systems Math. Biosci. 65 13-50
    • (1983) Math. Biosci. , vol.65 , pp. 13-50
    • Rai, B.1    Freedman, H.I.2    Addicott, J.F.3
  • 16
    • 38249033242 scopus 로고
    • A reaction-diffusion system of a competitor-competitor-mutualist model
    • Zheng S 1987 A reaction-diffusion system of a competitor-competitor-mutualist model J. Math. Anal. Appl. 124 254-80
    • (1987) J. Math. Anal. Appl. , vol.124 , pp. 254-280
    • Zheng, S.1
  • 17
    • 0001355473 scopus 로고
    • Asymptotic behavior of solutions of a periodic reaction-diffusion system of a competitor-competitor-mutualist model
    • Tineo A 1994 Asymptotic behavior of solutions of a periodic reaction-diffusion system of a competitor-competitor-mutualist model J. Diff. Eqns 108 326-41
    • (1994) J. Diff. Eqns , vol.108 , pp. 326-341
    • Tineo, A.1
  • 18
    • 0242376145 scopus 로고    scopus 로고
    • Geometric study of the asymptotic behavior of a periodic competitor-competitor-mutualist model
    • Tineo A 1997 Geometric study of the asymptotic behavior of a periodic competitor-competitor-mutualist model Nonlinear Stud. 4 69-80
    • (1997) Nonlinear Stud. , vol.4 , pp. 69-80
    • Tineo, A.1
  • 19
    • 0031062218 scopus 로고    scopus 로고
    • Three-dimensional periodic system with trivial dynamics II
    • Tineo A 1997 Three-dimensional periodic system with trivial dynamics II J. Math. Anal. Appl. 206 333-44
    • (1997) J. Math. Anal. Appl. , vol.206 , pp. 333-344
    • Tineo, A.1
  • 20
    • 0031237860 scopus 로고    scopus 로고
    • Global asymptotic behavior in a periodic competitor-competitor-mutualist parabolic system
    • Zhao X 1997 Global asymptotic behavior in a periodic competitor-competitor-mutualist parabolic system Nonlinear Anal. Ser. A: Theory Methods 29 551-68
    • (1997) Nonlinear Anal. Ser. A: Theory Methods , vol.29 , pp. 551-568
    • Zhao, X.1
  • 21
    • 0001634092 scopus 로고    scopus 로고
    • Positive periodic solutions of acompetitor-competitor-mutualist model
    • Du Y 1996 Positive periodic solutions of acompetitor-competitor-mutualist model Diff. Integral Eqns 9 1043-66
    • (1996) Diff. Integral Eqns , vol.9 , pp. 1043-1066
    • Du, Y.1
  • 22
    • 0035508060 scopus 로고    scopus 로고
    • Persistence in a periodic competitor-competitor-mutualist diffusion system
    • Fu S and Cui S 2001 Persistence in a periodic competitor-competitor-mutualist diffusion system J. Math. Anal. Appl. 263 234-45
    • (2001) J. Math. Anal. Appl. , vol.263 , pp. 234-245
    • Fu, S.1    Cui, S.2
  • 23
    • 0034311330 scopus 로고    scopus 로고
    • Periodic solutions of parabolic systems with time delays
    • Pao C V 2000 Periodic solutions of parabolic systems with time delays J. Math. Anal. Appl. 251 251-63
    • (2000) J. Math. Anal. Appl. , vol.251 , pp. 251-263
    • Pao, C.V.1
  • 24
    • 0034172560 scopus 로고    scopus 로고
    • Periodic solutions of systems of parabolic equations in unbounded domains
    • Lakshmikantham's legacy: a tribute on his 75th birthday
    • Pao C V 2000 Periodic solutions of systems of parabolic equations in unbounded domains. Lakshmikantham's legacy: a tribute on his 75th birthday Nonlinear Anal. Ser. A: Theory Methods 40 523-35
    • (2000) Nonlinear Anal. Ser. A: Theory Methods , vol.40 , pp. 523-535
    • Pao, C.V.1
  • 25
    • 0000919241 scopus 로고    scopus 로고
    • Periodic solutions of parabolic systems with nonlinear boundary conditions
    • Pao C V 1999 Periodic solutions of parabolic systems with nonlinear boundary conditions J. Math. Anal. Appl. 234 695-716
    • (1999) J. Math. Anal. Appl. , vol.234 , pp. 695-716
    • Pao, C.V.1
  • 26
    • 0027796995 scopus 로고
    • Hopf bifurcations in competitive three-dimensional Lotka-Volterra systems
    • Zeeman M L 1993 Hopf bifurcations in competitive three-dimensional Lotka-Volterra systems Dyn. Stab. Sys. 3 190-217
    • (1993) Dyn. Stab. Sys. , vol.3 , pp. 190-217
    • Zeeman, M.L.1
  • 28
    • 84990581010 scopus 로고
    • Differential equation models of some parasitic infections: Methods for the study of asymptotic behavior
    • Hirsch W M, Hanisch H and Gabriel J 1985 Differential equation models of some parasitic infections: methods for the study of asymptotic behavior Commun. Pure Appl. Math. 38 733-53
    • (1985) Commun. Pure Appl. Math. , vol.38 , pp. 733-753
    • Hirsch, W.M.1    Hanisch, H.2    Gabriel, J.3
  • 29
    • 21744446701 scopus 로고    scopus 로고
    • The global stability of a system modeling a community with limited competition
    • Jiang J 1997 The global stability of a system modeling a community with limited competition Proc. Am. Math. Soc. 125 1381-9
    • (1997) Proc. Am. Math. Soc. , vol.125 , pp. 1381-1389
    • Jiang, J.1
  • 30
    • 0242313115 scopus 로고    scopus 로고
    • Convergence in cooperative models with a weak concavity assumption
    • Jiang J 1999 Convergence in cooperative models with a weak concavity assumption Chin. J. Contemp. Math. 20 289-300
    • (1999) Chin. J. Contemp. Math. , vol.20 , pp. 289-300
    • Jiang, J.1
  • 31
    • 0022736370 scopus 로고
    • On the asymptotic behavior of a class of deterministic models of cooperating species
    • Smith H L 1986 On the asymptotic behavior of a class of deterministic models of cooperating species SIAM J. Appl. Math. 46 368-75
    • (1986) SIAM J. Appl. Math. , vol.46 , pp. 368-375
    • Smith, H.L.1
  • 32
    • 0001494541 scopus 로고
    • Three types of matrix stability
    • Cross G W 1978 Three types of matrix stability Linear Algebra Appl. 20 253-63
    • (1978) Linear Algebra Appl. , vol.20 , pp. 253-263
    • Cross, G.W.1
  • 34
    • 0036887505 scopus 로고    scopus 로고
    • The long-run behavior of periodic competitive Kolmogorov systems, nonlinear analysis
    • Wang Y and Jiang J 2002 The long-run behavior of periodic competitive Kolmogorov systems, nonlinear analysis Real World Appl. 3 471-85
    • (2002) Real World Appl. , vol.3 , pp. 471-485
    • Wang, Y.1    Jiang, J.2
  • 35
    • 0037059089 scopus 로고    scopus 로고
    • Uniqueness and attractivity of the carrying simples for the discrete-time competitive dynamical systems
    • Wang Y and Jiang J 2002 Uniqueness and attractivity of the carrying simples for the discrete-time competitive dynamical systems J. Diff. Eqns 186 611-32
    • (2002) J. Diff. Eqns , vol.186 , pp. 611-632
    • Wang, Y.1    Jiang, J.2
  • 38
    • 84968521825 scopus 로고
    • Periods of periodic solutions and the Lipschitz constant
    • Yorke J 1969 Periods of periodic solutions and the Lipschitz constant Proc. Am. Math. Soc. 22 509-12
    • (1969) Proc. Am. Math. Soc. , vol.22 , pp. 509-512
    • Yorke, J.1
  • 39
    • 4243550804 scopus 로고
    • Domains of attraction of generic ω-limit sets for strongly monotone discrete-time semigroups
    • Takáč P 1992 Domains of attraction of generic ω-limit sets for strongly monotone discrete-time semigroups J. Reine Angew. Math. 423 101-73
    • (1992) J. Reine Angew. Math. , vol.423 , pp. 101-173
    • Takáč, P.1
  • 40
    • 34249916235 scopus 로고
    • Convergence to cycles as a typical asymptotic behavior in smooth strongly monotone discrete-time dynamical systems
    • Poláčk P and Tereščák I 1991 Convergence to cycles as a typical asymptotic behavior in smooth strongly monotone discrete-time dynamical systems Arch. Rat. Mech. Anal. 116 339-60
    • (1991) Arch. Rat. Mech. Anal. , vol.116 , pp. 339-360
    • Poláčk, P.1    Tereščák, I.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.