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Volumn 32, Issue 3, 1998, Pages 381-408

Global analyses in some delayed ratio-dependent predator-prey systems

Author keywords

Global stability; Liapunov functional; Permanence; Predator prey system; Time delay

Indexed keywords

ASYMPTOTIC STABILITY; FUNCTIONS; LYAPUNOV METHODS; MATHEMATICAL MODELS; THEOREM PROVING;

EID: 0032058512     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(97)00491-4     Document Type: Article
Times cited : (234)

References (32)
  • 1
    • 0027075622 scopus 로고
    • The origins and evolution of predator-prey theory
    • Berryman, A. A., The origins and evolution of predator-prey theory. Ecology, 1992, 73, 1530-1535.
    • (1992) Ecology , vol.73 , pp. 1530-1535
    • Berryman, A.A.1
  • 2
    • 0002861760 scopus 로고
    • Uniqueness of limit cycles in Gause-type predator-prey systems
    • Kuang, Y. and Freedman, H. I., Uniqueness of limit cycles in Gause-type predator-prey systems. Math. Biosci., 1988, 88, 67-84.
    • (1988) Math. Biosci. , vol.88 , pp. 67-84
    • Kuang, Y.1    Freedman, H.I.2
  • 3
    • 84972834610 scopus 로고
    • Nonuniqueness of limit cycles of Gause-type predator-prey systems
    • Kuang, Y., Nonuniqueness of limit cycles of Gause-type predator-prey systems. Appl. Anal., 1988, 29, 269-287.
    • (1988) Appl. Anal. , vol.29 , pp. 269-287
    • Kuang, Y.1
  • 4
    • 38249025380 scopus 로고
    • On the location and period of limit cycles in Gause-type predator-prey systems
    • Kuang, Y., On the location and period of limit cycles in Gause-type predator-prey systems. J. Math. Anal. Appl., 1989, 142, 130-143.
    • (1989) J. Math. Anal. Appl. , vol.142 , pp. 130-143
    • Kuang, Y.1
  • 5
    • 0042448303 scopus 로고
    • Limit cycles in a chemostat-related model
    • Kuang, Y., Limit cycles in a chemostat-related model. SIAM J. Appl. Math., 1989, 49, 1759-1767.
    • (1989) SIAM J. Appl. Math. , vol.49 , pp. 1759-1767
    • Kuang, Y.1
  • 6
    • 0000671790 scopus 로고
    • Global stability of Gause-type predator-prey systems
    • Kuang, Y., Global stability of Gause-type predator-prey systems. J. Math. Biol., 1990, 28, 463-474.
    • (1990) J. Math. Biol. , vol.28 , pp. 463-474
    • Kuang, Y.1
  • 7
    • 0030589781 scopus 로고    scopus 로고
    • Convergence results in a well known delayed predator-prey system
    • Beretta, E. and Kuang, Y., Convergence results in a well known delayed predator-prey system. J. Math. Anal. Appl., 1996, 204, 840-853.
    • (1996) J. Math. Anal. Appl. , vol.204 , pp. 840-853
    • Beretta, E.1    Kuang, Y.2
  • 8
    • 0001030091 scopus 로고
    • Community structure, population control and competition
    • Hairston, N. G., Smith, F. E. and Slobodkin, L. B., Community structure, population control and competition. American Naturalist, 1960, 94, 421-425.
    • (1960) American Naturalist , vol.94 , pp. 421-425
    • Hairston, N.G.1    Smith, F.E.2    Slobodkin, L.B.3
  • 9
    • 0015243940 scopus 로고
    • Paradox of enrichment: Destabilization of exploitation systems in ecological time
    • Rosenzweig, M. L., Paradox of enrichment: destabilization of exploitation systems in ecological time. Science, 1969, 171, 385-387.
    • (1969) Science , vol.171 , pp. 385-387
    • Rosenzweig, M.L.1
  • 10
    • 0025251336 scopus 로고
    • Evaluation of natural enemies for biological control: A behavior approach
    • Luck, R. F., Evaluation of natural enemies for biological control: a behavior approach. Trends in Ecology and Evolution, 1990, 5, 196-199.
    • (1990) Trends in Ecology and Evolution , vol.5 , pp. 196-199
    • Luck, R.F.1
  • 12
    • 4944258042 scopus 로고
    • Coupling in predator-prey dynamics: Ratio-dependence
    • Arditi, R. and Ginzburg, L. R., Coupling in predator-prey dynamics: ratio-dependence. J. Theoretical Biology, 1989, 139, 311-326.
    • (1989) J. Theoretical Biology , vol.139 , pp. 311-326
    • Arditi, R.1    Ginzburg, L.R.2
  • 14
    • 0027100815 scopus 로고
    • Empirical evidence of the role of heterogeneity in ratio-dependent consumption
    • Arditi, R. and Saiah, H., Empirical evidence of the role of heterogeneity in ratio-dependent consumption. Ecology, 1992, 73, 1544-1551.
    • (1992) Ecology , vol.73 , pp. 1544-1551
    • Arditi, R.1    Saiah, H.2
  • 15
    • 0021257398 scopus 로고
    • Population dynamics: A per-capita resource approach
    • Getz, W. M., Population dynamics: a per-capita resource approach. J. Theoretical Biology, 1984, 108, 623-643.
    • (1984) J. Theoretical Biology , vol.108 , pp. 623-643
    • Getz, W.M.1
  • 16
    • 0001397558 scopus 로고
    • The functional response of predator: Worries about scale
    • Hanski, I., The functional response of predator: worries about scale; TREE, 1991, 6, 141-142.
    • (1991) TREE , vol.6 , pp. 141-142
    • Hanski, I.1
  • 17
    • 0000542895 scopus 로고
    • Variation in plankton densities among lakes: A case for ratio-dependent models
    • Arditi, R., Ginzburg, L. R. and Akcakaya, H. R., Variation in plankton densities among lakes: a case for ratio-dependent models. Am. Nat., 1991, 138, 1287-1296.
    • (1991) Am. Nat. , vol.138 , pp. 1287-1296
    • Arditi, R.1    Ginzburg, L.R.2    Akcakaya, H.R.3
  • 18
    • 0025946035 scopus 로고
    • Functional responses and heterogeneities: An experimental test with cladocerans
    • Arditi, R., Perrin, N. and Saiah, H., Functional responses and heterogeneities: an experimental test with cladocerans. OIKOS, 1991, 60, 69-75.
    • (1991) OIKOS , vol.60 , pp. 69-75
    • Arditi, R.1    Perrin, N.2    Saiah, H.3
  • 19
    • 0027098565 scopus 로고
    • Consequences of ratio-dependent predation for steady state properties of ecosystems
    • Ginzburg, L. R. and Akcakaya, H. R., Consequences of ratio-dependent predation for steady state properties of ecosystems. Ecology, 1992, 73, 1536-1543.
    • (1992) Ecology , vol.73 , pp. 1536-1543
    • Ginzburg, L.R.1    Akcakaya, H.R.2
  • 21
    • 0000301505 scopus 로고
    • The stability and the intrinsic growth rates of prey and predator populations
    • Tanner, J. T., The stability and the intrinsic growth rates of prey and predator populations. Ecology, 1975, 56, 855-867.
    • (1975) Ecology , vol.56 , pp. 855-867
    • Tanner, J.T.1
  • 23
    • 0029325665 scopus 로고
    • Global stability for a class of predator-prey systems
    • Hsu, S.-B. and Huang, T.-W., Global stability for a class of predator-prey systems. SIAM J. Appl. Math., 1995, 55, 763-783.
    • (1995) SIAM J. Appl. Math. , vol.55 , pp. 763-783
    • Hsu, S.-B.1    Huang, T.-W.2
  • 25
    • 0001283921 scopus 로고
    • Stability switches in linear scalar neutral delay equations
    • Freedman, H. I. and Kuang, Y., Stability switches in linear scalar neutral delay equations. Funkcialaj Ekvacioj, 1991, 34, 187-209.
    • (1991) Funkcialaj Ekvacioj , vol.34 , pp. 187-209
    • Freedman, H.I.1    Kuang, Y.2
  • 26
    • 0012193361 scopus 로고
    • Convergence in Lotka-Volterra type delay systems without instantaneous feedbacks
    • Kuang, Y. and Smith, H. L., Convergence in Lotka-Volterra type delay systems without instantaneous feedbacks. Proc. Roy. Soc. Edinburgh, 1993, 123A, 45-58.
    • (1993) Proc. Roy. Soc. Edinburgh , vol.123 A , pp. 45-58
    • Kuang, Y.1    Smith, H.L.2
  • 27
    • 0001197579 scopus 로고
    • Convergence in Lotka-Volterra type diffusive delay systems without dominating instantaneous negative feedbacks
    • Kuang, Y. and Smith, H. L., Convergence in Lotka-Volterra type diffusive delay systems without dominating instantaneous negative feedbacks. J. Austral. Math. Soc. Ser. B., 1993, 34, 471-493.
    • (1993) J. Austral. Math. Soc. Ser. B. , vol.34 , pp. 471-493
    • Kuang, Y.1    Smith, H.L.2
  • 28
    • 0000731675 scopus 로고
    • Global stability in delay differential systems without dominating instantaneous negative feedbacks
    • Kuang, Y., Global stability in delay differential systems without dominating instantaneous negative feedbacks. J. Diff. Eqns., 1995, 119, 503-532.
    • (1995) J. Diff. Eqns. , vol.119 , pp. 503-532
    • Kuang, Y.1
  • 29
    • 0001503284 scopus 로고
    • Coexistence in a model of competition in the chemostat incorporating discrete delays
    • Freedman, H. I., So. J. W.-H. and Waltman, P., Coexistence in a model of competition in the chemostat incorporating discrete delays. SIAM J. Appl. Math., 1989, 49, 859-870.
    • (1989) SIAM J. Appl. Math. , vol.49 , pp. 859-870
    • Freedman, H.I.1    So, J.W.-H.2    Waltman, P.3
  • 30
    • 0001864149 scopus 로고
    • Qualitative properties of chemostat equations with time delays: Boundedness, local and global asymptotic stability
    • Beretta, E. and Takeuchi, Y., Qualitative properties of chemostat equations with time delays: boundedness, local and global asymptotic stability. Differential Equations and Dynamical Systems, 1994, 2, 19-40.
    • (1994) Differential Equations and Dynamical Systems , vol.2 , pp. 19-40
    • Beretta, E.1    Takeuchi, Y.2
  • 31
    • 0000128494 scopus 로고
    • Qualitative properties of chemostat equations with time delays - II. Differential
    • Beretta, E. and Takeuchi, Y., Qualitative properties of chemostat equations with time delays - II. Differential Equations and Dynamical Systems, 1994, 2, 263-288.
    • (1994) Equations and Dynamical Systems , vol.2 , pp. 263-288
    • Beretta, E.1    Takeuchi, Y.2
  • 32
    • 0011678840 scopus 로고
    • Global stability for chemostat equations with delayed nutrient recycling
    • Beretta, E. and Takeuchi, Y., Global stability for chemostat equations with delayed nutrient recycling. Nonlinear World, 1994, 1, 291-306.
    • (1994) Nonlinear World , vol.1 , pp. 291-306
    • Beretta, E.1    Takeuchi, Y.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.