메뉴 건너뛰기




Volumn 205, Issue 1, 2004, Pages 50-76

Dynamics of the periodic type-K competitive Kolmogorov systems

Author keywords

Exponential separation; Invariant order decomposition; Persistence; Pesin's theory; Poincar map; Time periodic type K competitive system

Indexed keywords


EID: 4344669710     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jde.2004.06.020     Document Type: Article
Times cited : (17)

References (46)
  • 2
    • 0001634092 scopus 로고    scopus 로고
    • Positive periodic solutions of a competitor - Competitor-mutualist model
    • Y. Du Positive periodic solutions of a competitor - Competitor-mutualist model Differential Integral Equations 9 1996 1043-1066
    • (1996) Differential Integral Equations , vol.9 , pp. 1043-1066
    • Du, Y.1
  • 3
    • 0016070051 scopus 로고
    • Asymptotic stability with rate conditions
    • N. Fenichel Asymptotic stability with rate conditions Indiana Univ. Math. J. 23 1974 1109-1137
    • (1974) Indiana Univ. Math. J. , vol.23 , pp. 1109-1137
    • Fenichel, N.1
  • 4
    • 0010463272 scopus 로고
    • Unified mechanism for relay and oscillation of cyclic AMP in Distyostelium discoideum
    • A. Goldbeter L. Segel Unified mechanism for relay and oscillation of cyclic AMP in Distyostelium discoideum Proc. Nat. Acad. Sci. USA 74 1977 1543-1547
    • (1977) Proc. Nat. Acad. Sci. USA , vol.74 , pp. 1543-1547
    • Goldbeter, A.1    Segel, L.2
  • 5
    • 0028974350 scopus 로고
    • Comparing predator-prey models to Luckinbill's experiment with Didinium and Paramecium
    • G. Harrison Comparing predator-prey models to Luckinbill's experiment with Didinium and Paramecium Ecology 76 1995 357-374
    • (1995) Ecology , vol.76 , pp. 357-374
    • Harrison, G.1
  • 6
    • 21144459956 scopus 로고
    • Boundedness of prime periods of stable cycles and convergence to fixed point in discrete monotone dynamical systems
    • P. Hess P. Poláčik Boundedness of prime periods of stable cycles and convergence to fixed point in discrete monotone dynamical systems Math. Anal. 24 1993 1312-1330
    • (1993) SIAM J. Math. Anal. , vol.24 , pp. 1312-1330
    • Hess, P.1    Poláčik, P.2
  • 7
    • 0000885375 scopus 로고
    • Systems of differential equations which are competitive or cooperative, I: Limit sets
    • M.W. Hirsch Systems of differential equations which are competitive or cooperative, I: limit sets Math. Anal. 13 1982 167-179
    • (1982) SIAM J. Math. Anal. , vol.13 , pp. 167-179
    • Hirsch, M.W.1
  • 8
    • 0001176145 scopus 로고
    • Systems of differential equations that are competitive or cooperative, II: Convergence almost everywhere
    • M.W. Hirsch Systems of differential equations that are competitive or cooperative, II: Convergence almost everywhere Math. Anal. 16 1985 423-439
    • (1985) SIAM J. Math. Anal. , vol.16 , pp. 423-439
    • Hirsch, M.W.1
  • 9
    • 84956106116 scopus 로고
    • Systems of differential equations which are competitive or cooperative, III: Competing species
    • M.W. Hirsch Systems of differential equations which are competitive or cooperative, III: Competing species Nonlinearity 1 1988 51-71
    • (1988) Nonlinearity , vol.1 , pp. 51-71
    • Hirsch, M.W.1
  • 10
    • 33745815315 scopus 로고
    • Stability and convergence in strongly monotone dynamical systems
    • M.W. Hirsch Stability and convergence in strongly monotone dynamical systems J. Reine Angew. Math. 383 1988 1-53
    • (1988) J. Reine Angew. Math. , vol.383 , pp. 1-53
    • Hirsch, M.W.1
  • 11
    • 0001015290 scopus 로고
    • Systems of differential equations that are competitive or cooperative, IV: Structural stability in three-dimensional systems
    • M.W. Hirsch Systems of differential equations that are competitive or cooperative, IV: Structural stability in three-dimensional systems Math. Anal. 21 1990 1225-12349
    • (1990) SIAM J. Math. Anal. , vol.21 , pp. 1225-12349
    • Hirsch, M.W.1
  • 12
    • 0000317364 scopus 로고    scopus 로고
    • Chain transitive sets for smooth strongly monotone dynamical systems
    • M. Hirsch Chain transitive sets for smooth strongly monotone dynamical systems Dyn. Discrete Continuous Impulsive Systems 5 1999 529-543
    • (1999) Dyn. Discrete Continuous Impulsive Systems , vol.5 , pp. 529-543
    • Hirsch, M.1
  • 13
    • 0000044573 scopus 로고
    • Stable manifolds and hyperbolic sets
    • American Mathematical Society Providence, RI
    • M.W. Hirsch C.C. Pugh Stable manifolds and hyperbolic sets Proceeding of the Symposia in Pure Mathematics, vol. 14 1970 American Mathematical Society Providence, RI 133-163
    • (1970) Proceeding of the Symposia in Pure Mathematics , pp. 133-163
    • Hirsch, M.W.1    Pugh, C.C.2
  • 16
    • 0036721857 scopus 로고    scopus 로고
    • On the finite dimensional dynamical systems with limited competition
    • X. Liang J. Jiang On the finite dimensional dynamical systems with limited competition Trans. Amer. Math. Soc. 354 2002 3535-3554
    • (2002) Trans. Amer. Math. Soc. , vol.354 , pp. 3535-3554
    • Liang, X.1    Jiang, J.2
  • 17
    • 0037457045 scopus 로고    scopus 로고
    • Discrete infinite dimensional Type-K monotone dynamical systems and time periodic reaction-diffusion systems
    • X. Liang J. Jiang Discrete infinite dimensional Type-K monotone dynamical systems and time periodic reaction-diffusion systems J. Differential Equations 189 2003 318-354
    • (2003) J. Differential Equations , vol.189 , pp. 318-354
    • Liang, X.1    Jiang, J.2
  • 18
    • 0242371799 scopus 로고    scopus 로고
    • The dynamical behavior of Type-K competitive Kolmogorov systems and its application to 3-dimensional Type-K competitive Lotka - Volterra systems
    • X. Liang J. Jiang The dynamical behavior of Type-K competitive Kolmogorov systems and its application to 3-dimensional Type-K competitive Lotka - Volterra systems Nonlinearity 16 2003 785-801
    • (2003) Nonlinearity , vol.16 , pp. 785-801
    • Liang, X.1    Jiang, J.2
  • 20
    • 4243841547 scopus 로고
    • The C1 property of carrying simplices for a competitive systems of ODEs
    • J. Mierczyński The C 1 property of carrying simplices for a competitive systems of ODEs J. Differential Equations 111 1994 385-409
    • (1994) J. Differential Equations , vol.111 , pp. 385-409
    • Mierczyński, J.1
  • 21
    • 84972500224 scopus 로고
    • p-arcs in strongly monotone discrete-time dynamical systems
    • J. Mierczyński p-arcs in strongly monotone discrete-time dynamical systems Differential Integral Equations 7 1994 1473-1494
    • (1994) Differential Integral Equations , vol.7 , pp. 1473-1494
    • Mierczyński, J.1
  • 23
    • 34249916235 scopus 로고
    • Convergence to cycles as a typical asymptotic behavior in smoothly monotone discrete-time dynamical systems
    • P. Poláčik I. Tereščák Convergence to cycles as a typical asymptotic behavior in smoothly monotone discrete-time dynamical systems Arch. Rational Mech. Anal. 116 1991 339-360
    • (1991) Arch. Rational Mech. Anal. , vol.116 , pp. 339-360
    • Poláčik, P.1    Tereščák, I.2
  • 24
    • 0002460864 scopus 로고
    • Analysis of three-species models of mutualism in predator-prey and competitive systems
    • B. Rai H.I. Freedman J. Addicott Analysis of three-species models of mutualism in predator-prey and competitive systems Math. Biosci. 65 1983 13-50
    • (1983) Math. Biosci. , vol.65 , pp. 13-50
    • Rai, B.1    Freedman, H.I.2    Addicott, J.3
  • 25
    • 51649166261 scopus 로고
    • Ergodic theory of differentiable dynamical systems
    • D. Ruelle Ergodic theory of differentiable dynamical systems Inst. Hautes Études Sci Publ. Math. 50 1979 27-58
    • (1979) Inst. Hautes Études Sci Publ. Math. , vol.50 , pp. 27-58
    • Ruelle, D.1
  • 26
    • 0002890056 scopus 로고
    • Analyticity properties of the characteristic exponents of random matrix products
    • D. Ruelle Analyticity properties of the characteristic exponents of random matrix products Adv. in Math. 32 1 1979 68-80
    • (1979) Adv. in Math. , vol.32 , Issue.1 , pp. 68-80
    • Ruelle, D.1
  • 27
    • 0017256150 scopus 로고
    • On the differential equations of species in competition
    • S. Smale On the differential equations of species in competition J. Math. Biol. 3 1976 5-7
    • (1976) J. Math. Biol. , vol.3 , pp. 5-7
    • Smale, S.1
  • 28
    • 38249038749 scopus 로고
    • Periodic competitive differential equations and the discrete dynamics of competitive maps
    • H.L. Smith Periodic competitive differential equations and the discrete dynamics of competitive maps J. Differential Equations 64 1986 165-194
    • (1986) J. Differential Equations , vol.64 , pp. 165-194
    • Smith, H.L.1
  • 29
    • 0000743387 scopus 로고
    • Competing subcommunities of mutualists and a generalized Kamke theorem
    • H.L. Smith Competing subcommunities of mutualists and a generalized Kamke theorem Appl. Math. 46 1986 856-874
    • (1986) SIAM J. Appl. Math. , vol.46 , pp. 856-874
    • Smith, H.L.1
  • 30
    • 0038840779 scopus 로고
    • Invariant curves for mappings
    • H.L. Smith Invariant curves for mappings Math. Anal. 17 1986 1053-1067
    • (1986) SIAM J. Math. Anal. , vol.17 , pp. 1053-1067
    • Smith, H.L.1
  • 32
    • 4344574613 scopus 로고    scopus 로고
    • Dynamics of competition
    • V. Capasso, O. Diekmann (Eds.) Springer, Berlin, Heidelberg, New York
    • H.L. Smith, Dynamics of competition, in: V. Capasso, O. Diekmann (Eds.), Mathematics Inspired by Biology Lecture Notes in Mathematics, vol. 1714, Springer, Berlin, Heidelberg, New York, 1999, 191-240.
    • (1999) Mathematics Inspired By Biology Lecture Notes in Mathematics , vol.1714 , pp. 191-240
    • Smith, H.L.1
  • 33
    • 0035841057 scopus 로고    scopus 로고
    • Stable coexistence and bi-stability for competitive systems on ordered Banach spaces
    • H.L. Smith H.R. Thieme Stable coexistence and bi-stability for competitive systems on ordered Banach spaces J. Differential Equations 176 2001 195-222
    • (2001) J. Differential Equations , vol.176 , pp. 195-222
    • Smith, H.L.1    Thieme, H.R.2
  • 35
    • 0001355473 scopus 로고
    • Asymptotic behavior of solutions of a periodic reaction - Diffusion system of a competitor - Competitor-mutualist model
    • A. Tineo Asymptotic behavior of solutions of a periodic reaction - Diffusion system of a competitor - Competitor-mutualist model J. Differential Equations 108 1994 326-341
    • (1994) J. Differential Equations , vol.108 , pp. 326-341
    • Tineo, A.1
  • 36
    • 0025425054 scopus 로고
    • Convergence to equilibrium on invariant d-hypersurfaces for strongly increasing discrete-time semigroups
    • P. Takáč Convergence to equilibrium on invariant d -hypersurfaces for strongly increasing discrete-time semigroups J. Math. Anal. Appl. 148 1990 223-244
    • (1990) J. Math. Anal. Appl. , vol.148 , pp. 223-244
    • Takáč, P.1
  • 37
    • 4243550804 scopus 로고
    • Domains of attraction of generic ω-limit sets for strongly monotone discrete-time semigroups
    • P. Takáč Domains of attraction of generic ω -limit sets for strongly monotone discrete-time semigroups J. Reine Angew. Math. 423 1992 101-173
    • (1992) J. Reine Angew. Math. , vol.423 , pp. 101-173
    • Takáč, P.1
  • 38
    • 0003479527 scopus 로고    scopus 로고
    • 1 smooth strongly monotone discrete-time dynamical systems
    • preprint
    • 1 smooth strongly monotone discrete-time dynamical systems, preprint,
    • (1996)
    • Tereščák, I.1
  • 39
    • 0032623132 scopus 로고    scopus 로고
    • Global stability and permanence for a class of type K monotone systems
    • C. Tu J. Jiang Global stability and permanence for a class of type K monotone systems Math. Anal. 30 1999 360-378
    • (1999) SIAM J. Math. Anal. , vol.30 , pp. 360-378
    • Tu, C.1    Jiang, J.2
  • 40
    • 0035506703 scopus 로고    scopus 로고
    • The general properties of discrete-time competitive dynamical systems
    • Y. Wang J. Jiang The general properties of discrete-time competitive dynamical systems J. Differential Equations 176 2001 470-493
    • (2001) J. Differential Equations , vol.176 , pp. 470-493
    • Wang, Y.1    Jiang, J.2
  • 41
    • 0036887505 scopus 로고    scopus 로고
    • The long-run behavior of periodic competitive Kolmogorov systems
    • Y. Wang J. Jiang The long-run behavior of periodic competitive Kolmogorov systems Nonlinear Anal.: Real World Appl. 3 2002 471-485
    • (2002) Nonlinear Anal.: Real World Appl. , vol.3 , pp. 471-485
    • Wang, Y.1    Jiang, J.2
  • 42
    • 0037059089 scopus 로고    scopus 로고
    • Uniqueness and attractivity of the carrying simplices for the discrete-time competitive dynamical systems
    • Y. Wang J. Jiang Uniqueness and attractivity of the carrying simplices for the discrete-time competitive dynamical systems J. Differential Equations 186 2002 611-632
    • (2002) J. Differential Equations , vol.186 , pp. 611-632
    • Wang, Y.1    Jiang, J.2
  • 43
    • 0027796995 scopus 로고
    • Hopf bifurcations in competitive three-dimensional Lotka - Volterra systems
    • M.L. Zeeman Hopf bifurcations in competitive three-dimensional Lotka - Volterra systems Dyn. Stability Systems 8 1993 189-217
    • (1993) Dyn. Stability Systems , vol.8 , pp. 189-217
    • Zeeman, M.L.1
  • 44
    • 0031237860 scopus 로고    scopus 로고
    • Global asymptotic behavior in a periodic competitor - Competitor-mutualist parabolic system
    • X.-Q. Zhao Global asymptotic behavior in a periodic competitor - Competitor-mutualist parabolic system Nonlinear Anal. 29 1997 551-568
    • (1997) Nonlinear Anal. , vol.29 , pp. 551-568
    • Zhao, X.-Q.1
  • 46
    • 4344711898 scopus 로고    scopus 로고
    • Smoothness of the carrying simplex for the discrete-time competitive dynamical systems
    • preprint
    • J. Jiang, J. Mierczński, Yi Wang, Smoothness of the carrying simplex for the discrete-time competitive dynamical systems, preprint, 2004.
    • (2004)
    • Jiang, J.1    Mierczński, J.2    Wang, Y.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.