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Volumn 66, Issue 4, 2006, Pages 1101-1129

A stage-structured predator-prey model of Beddington-DeAngelis type

Author keywords

Beddington DeAngelis; Delay; Predator prey; Stage structure

Indexed keywords

MATHEMATICAL MODELS; NUMERICAL METHODS; ROBUSTNESS (CONTROL SYSTEMS); SYSTEM STABILITY;

EID: 33747198005     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/050630003     Document Type: Article
Times cited : (151)

References (41)
  • 1
    • 0025132577 scopus 로고
    • A time-delay model of single-species growth with stage structure
    • W. AIELLO AND H. I. FREEDMAN, A time-delay model of single-species growth with stage structure, Math. Biosci., 101 (1990), pp. 139-153.
    • (1990) Math. Biosci. , vol.101 , pp. 139-153
    • Aiello, W.1    Freedman, H.I.2
  • 2
    • 1642421831 scopus 로고    scopus 로고
    • Stability and traveling fronts in Lotka-Volterra competition models with stage structure
    • J. AL-OMARI AND S. GOURLEY, Stability and traveling fronts in Lotka-Volterra competition models with stage structure, SIAM J. Appl. Math., 63 (2003), pp. 2063-2086.
    • (2003) SIAM J. Appl. Math. , vol.63 , pp. 2063-2086
    • Al-Omari, J.1    Gourley, S.2
  • 3
    • 4944258042 scopus 로고
    • Coupling in predator-prey dynamics: Ratio-dependence
    • R. ARDITI AND L. R. GINZBURG, Coupling in predator-prey dynamics: Ratio-dependence, J. Theoret. Biol., 1989 (139), pp. 311-326.
    • (1989) J. Theoret. Biol. , Issue.139 , pp. 311-326
    • Arditi, R.1    Ginzburg, L.R.2
  • 4
    • 0030403458 scopus 로고    scopus 로고
    • Invulnerable prey and the statics and dynamics of predatorprey interaction
    • P. A. ABRAMS AND C. J. WALTERS, Invulnerable prey and the statics and dynamics of predatorprey interaction, Ecology, 1996 (77), pp. 1125-1133.
    • (1996) Ecology , Issue.77 , pp. 1125-1133
    • Abrams, P.A.1    Walters, C.J.2
  • 5
    • 0034255819 scopus 로고    scopus 로고
    • The nature of predation: Prey dependent, ratio dependent or neither?
    • P. A. ABRAMS AND L. R. GINZBURG, The nature of predation: Prey dependent, ratio dependent or neither? TREE, 2000 (15), pp. 337-341.
    • (2000) TREE , Issue.15 , pp. 337-341
    • Abrams, P.A.1    Ginzburg, L.R.2
  • 6
    • 0000076167 scopus 로고
    • Mutual interference between parasites or predators and its effect on searching efficiency
    • J. R. BEDDINOTON, Mutual interference between parasites or predators and its effect on searching efficiency, J. Animal Ecol., 44 (1975), pp. 331-340.
    • (1975) J. Animal Ecol. , vol.44 , pp. 331-340
    • Beddinoton, J.R.1
  • 7
    • 0032058512 scopus 로고    scopus 로고
    • Global analysis in some delayed ratio-dependent predator-prey systems
    • E. BERETTA AND Y. KUANG, Global analysis in some delayed ratio-dependent predator-prey systems, Nonlinear Anal., 32 (1998), pp. 381-408.
    • (1998) Nonlinear Anal. , vol.32 , pp. 381-408
    • Beretta, E.1    Kuang, Y.2
  • 8
    • 0036373967 scopus 로고    scopus 로고
    • Geometric stability switch criteria in delay differential systems with delay dependent parameters
    • E. BERETTA AND Y. KUANG, Geometric stability switch criteria in delay differential systems with delay dependent parameters, SIAM J. Math. Anal., 33 (2002), pp. 1144-1165.
    • (2002) SIAM J. Math. Anal. , vol.33 , pp. 1144-1165
    • Beretta, E.1    Kuang, Y.2
  • 9
    • 0038750243 scopus 로고    scopus 로고
    • On the dynamics of predator-prey models with the Beddington-DeAngelis functional response
    • R. S. CANTRELL AND C. COSNER, On the dynamics of predator-prey models with the Beddington-DeAngelis functional response, J. Math. Anal. Appl., 257 (2001), pp. 206-222.
    • (2001) J. Math. Anal. Appl. , vol.257 , pp. 206-222
    • Cantrell, R.S.1    Cosner, C.2
  • 10
    • 2942685827 scopus 로고    scopus 로고
    • Intraspecific interference and consumer-resource dynamics
    • R. S. CANTRELL, C. COSNER, AND S. G. RUAN, Intraspecific interference and consumer-resource dynamics, Dyn. Syst. Ser. B, 4 (2004), pp. 527-546.
    • (2004) Dyn. Syst. Ser. B , vol.4 , pp. 527-546
    • Cantrell, R.S.1    Cosner, C.2    Ruan, S.G.3
  • 11
    • 0033180314 scopus 로고    scopus 로고
    • Effects of spatial grouping on the functional response of predators
    • C. COSNER, D. L. DEANGELIS, J. S. AULT, AND D. B. OLSON, Effects of spatial grouping on the functional response of predators, Theoret. Popul. Biol., 56 (1999), pp. 65-75.
    • (1999) Theoret. Popul. Biol. , vol.56 , pp. 65-75
    • Cosner, C.1    DeAngelis, D.L.2    Ault, J.S.3    Olson, D.B.4
  • 12
    • 0001156508 scopus 로고
    • Functional responses and interference within and between year classes of a dragonfly population
    • P. H. CROWLEY AND E. K. MARTIN, Functional responses and interference within and between year classes of a dragonfly population, J. North American Benthological Soc., 8 (1989), pp. 211-221.
    • (1989) J. North American Benthological Soc. , vol.8 , pp. 211-221
    • Crowley, P.H.1    Martin, E.K.2
  • 13
    • 0001657717 scopus 로고
    • A model for trophic interaction
    • D. L. DEANGELIS, R. A. GOLDSTEIN, AND R. NEILL, A model for trophic interaction, Ecology, 56 (1975), pp. 881-892.
    • (1975) Ecology , vol.56 , pp. 881-892
    • DeAngelis, D.L.1    Goldstein, R.A.2    Neill, R.3
  • 14
    • 2942641510 scopus 로고    scopus 로고
    • Dynamics of a nonautonomous predator prey system with the Beddington-DeAngelis functional response
    • M. FAN AND Y. KUANG, Dynamics of a nonautonomous predator prey system with the Beddington-DeAngelis functional response, J. Math. Anal. Appl., 295 (2004), pp. 15-39.
    • (2004) J. Math. Anal. Appl. , vol.295 , pp. 15-39
    • Fan, M.1    Kuang, Y.2
  • 15
    • 15844390604 scopus 로고    scopus 로고
    • A stage structured predator-prey model and its dependence on through-stage delay and death rate
    • S. A. GOURLEY AND Y. KUANG, A stage structured predator-prey model and its dependence on through-stage delay and death rate, J. Math. Biol., 49 (2004), pp. 188-200.
    • (2004) J. Math. Biol. , vol.49 , pp. 188-200
    • Gourley, S.A.1    Kuang, Y.2
  • 16
    • 0000802631 scopus 로고
    • Persistence in infinite-dimensional systems
    • J. K. HALE AND P. WALTMAN, Persistence in infinite-dimensional systems, SIAM J. Math. Anal., 20 (1989), pp. 388-395.
    • (1989) SIAM J. Math. Anal. , vol.20 , pp. 388-395
    • Hale, J.K.1    Waltman, P.2
  • 17
    • 0014673629 scopus 로고
    • New inductive population model for insect parasites and its bearing on biological control
    • M. P. HASSELL AND C. C. VARLEY, New inductive population model for insect parasites and its bearing on biological control, Nature, 223 (1969), pp. 1133-1137.
    • (1969) Nature , vol.223 , pp. 1133-1137
    • Hassell, M.P.1    Varley, C.C.2
  • 18
    • 0003324723 scopus 로고
    • Introduction to functional differential equations
    • Springer-Verlag, New York
    • J. K. HALE AND S. V. LUNEL, Introduction to Functional Differential Equations, Appl. Math. Sci. 99, Springer-Verlag, New York, 1993.
    • (1993) Appl. Math. Sci. , vol.99
    • Hale, J.K.1    Lunel, S.V.2
  • 19
    • 84888258034 scopus 로고
    • The components of predation as revealed by a study of small mammal predation of the European pine sawfly
    • C. S. HOLLING, The components of predation as revealed by a study of small mammal predation of the European pine sawfly, Canad. Entomologist, 91 (1959), pp. 293-320.
    • (1959) Canad. Entomologist , vol.91 , pp. 293-320
    • Holling, C.S.1
  • 20
    • 84880026161 scopus 로고
    • Some characteristics of simple types of predation and parasitism
    • C. S. HOLLING, Some characteristics of simple types of predation and parasitism, Canad. Entomologist, 91 (1959), pp. 385-395.
    • (1959) Canad. Entomologist , vol.91 , pp. 385-395
    • Holling, C.S.1
  • 21
    • 0000157634 scopus 로고
    • A contribution to the theory of competing predators
    • S. B. Hsu, S. P. HUBBELL, AND P. WALTMAN, A contribution to the theory of competing predators, Ecological Monogr., 35 (1978), pp. 617-625.
    • (1978) Ecological Monogr. , vol.35 , pp. 617-625
    • Hsu, S.B.1    Hubbell, S.P.2    Waltman, P.3
  • 23
    • 0037670816 scopus 로고    scopus 로고
    • Global analysis of the predator-prey system with Beddington-DeAngelis functional response
    • Z. W. H WANG, Global analysis of the predator-prey system with Beddington-DeAngelis functional response, J. Math. Anal. Appl., 281 (2003), pp. 395-401.
    • (2003) J. Math. Anal. Appl. , vol.281 , pp. 395-401
    • Wang, Z.W.H.1
  • 24
    • 1242344859 scopus 로고    scopus 로고
    • Uniqueness of limit cycles of the predator-prey system with Beddington-DeAngelis functional response
    • Z. W. HWANG, Uniqueness of limit cycles of the predator-prey system with Beddington-DeAngelis functional response, J. Math. Anal. Appl., 290 (2004), pp. 113-122
    • (2004) J. Math. Anal. Appl. , vol.290 , pp. 113-122
    • Hwang, Z.W.1
  • 25
    • 0000671790 scopus 로고
    • Global stability of Gause-type predator-prey systems
    • Y. KUANG, Global stability of Gause-type predator-prey systems, J. Math. Biol., 28 (1990), pp. 463-474.
    • (1990) J. Math. Biol. , vol.28 , pp. 463-474
    • Kuang, Y.1
  • 27
    • 0000252357 scopus 로고    scopus 로고
    • Global qualitative analysis of a ratio-dependent predator-prey system
    • Y. KUANG AND E. BERETTA, Global qualitative analysis of a ratio-dependent predator-prey system, J. Math. Biol., 36 (1998), pp. 389-406.
    • (1998) J. Math. Biol. , vol.36 , pp. 389-406
    • Kuang, Y.1    Beretta, E.2
  • 28
    • 0036659991 scopus 로고    scopus 로고
    • Asymptotic behavior of competitive Lotka-Volterra system with stage structure
    • S. LIU, L. CHEN, G. LUO, AND Y. JIANG, Asymptotic behavior of competitive Lotka-Volterra system with stage structure, J. Math. Anal. Appl., 271 (2002), pp. 124-138.
    • (2002) J. Math. Anal. Appl. , vol.271 , pp. 124-138
    • Liu, S.1    Chen, L.2    Luo, G.3    Jiang, Y.4
  • 29
    • 0037032855 scopus 로고    scopus 로고
    • Recent progress on stage-structured population dynamics
    • S. LIU, L. CHEN, AND R. AGARWAL, Recent progress on stage-structured population dynamics, Math. Comput. Modelling, 36 (2002), pp. 1319-1360.
    • (2002) Math. Comput. Modelling , vol.36 , pp. 1319-1360
    • Liu, S.1    Chen, L.2    Agarwal, R.3
  • 30
    • 0036883834 scopus 로고    scopus 로고
    • Extinction and permanence in competitive stage structured system with time delays
    • S. LIU, L. CHEN, AND G. LUO, Extinction and permanence in competitive stage structured system with time delays, Nonlinear Anal., 51 (2002), pp. 1347-1361.
    • (2002) Nonlinear Anal. , vol.51 , pp. 1347-1361
    • Liu, S.1    Chen, L.2    Luo, G.3
  • 31
    • 0037110188 scopus 로고    scopus 로고
    • Extinction and permanence in nonautonomous competitive system with stage structure
    • S. LIU, L. CHEN, AND Z. LIU, Extinction and permanence in nonautonomous competitive system with stage structure, J. Math. Anal. Appl., 274 (2002), pp. 667-684.
    • (2002) J. Math. Anal. Appl. , vol.274 , pp. 667-684
    • Liu, S.1    Chen, L.2    Liu, Z.3
  • 32
    • 10144219961 scopus 로고    scopus 로고
    • Permanence and global asymptotic stability in a stage structured system with distributed delays
    • S. LIU, M. KOUCHE, AND N. TATAR, Permanence and global asymptotic stability in a stage structured system with distributed delays, J. Math. Anal. Appl., 301 (2005), pp. 187-207.
    • (2005) J. Math. Anal. Appl. , vol.301 , pp. 187-207
    • Liu, S.1    Kouche, M.2    Tatar, N.3
  • 33
    • 3442890192 scopus 로고    scopus 로고
    • Stability and bifurcation in a delayed predator-prey system with Beddington-DeAngelis functional response
    • Z. Liu AND R. YUAN, Stability and bifurcation in a delayed predator-prey system with Beddington-DeAngelis functional response, J. Math. Anal. Appl., 296 (2004), pp. 521-537.
    • (2004) J. Math. Anal. Appl. , vol.296 , pp. 521-537
    • Liu, Z.1    Yuan, R.2
  • 34
    • 0035460603 scopus 로고    scopus 로고
    • Predator-prey models with delay and prey harvesting
    • A. MARTIN AND S. RUAN, Predator-prey models with delay and prey harvesting, J. Math. Biol., 43 (2001), pp. 247-267.
    • (2001) J. Math. Biol. , vol.43 , pp. 247-267
    • Martin, A.1    Ruan, S.2
  • 35
    • 0041729100 scopus 로고    scopus 로고
    • The asymptotic behaviors of a stage-structured autonomous predator-prey system with time delay
    • L. OU, G. LUO, Y. JIANG, AND Y. LI, The asymptotic behaviors of a stage-structured autonomous predator-prey system with time delay, J. Math. Anal. Appl., 283 (2003), pp. 534-548.
    • (2003) J. Math. Anal. Appl. , vol.283 , pp. 534-548
    • Ou, L.1    Luo, G.2    Jiang, Y.3    Li, Y.4
  • 36
    • 0346671147 scopus 로고    scopus 로고
    • The asymptotic behavior of a chemostat model with the Beddington-DeAngelis functional response
    • Z. P. QIU, J. YU, AND Y. ZOU, The asymptotic behavior of a chemostat model with the Beddington-DeAngelis functional response, Math. Biosci., 187 (2004), pp. 175-187.
    • (2004) Math. Biosci. , vol.187 , pp. 175-187
    • Qiu, Z.P.1    Yu, J.2    Zou, Y.3
  • 37
    • 0030986552 scopus 로고    scopus 로고
    • Predation and bark beetle longterm dynamics
    • J. D. REEVE, Predation and bark beetle longterm dynamics, Oecologia, 112 (1997), pp. 48-54.
    • (1997) Oecologia , vol.112 , pp. 48-54
    • Reeve, J.D.1
  • 39
    • 0035658752 scopus 로고    scopus 로고
    • Functional responses with predator interference: Viable alternatives to the Hailing type II model
    • G. T. SKALSKI AND J. F. GILLIAM, Functional responses with predator interference: Viable alternatives to the Hailing type II model, Ecology, 82 (2001), pp. 3083-3092.
    • (2001) Ecology , vol.82 , pp. 3083-3092
    • Skalski, G.T.1    Gilliam, J.F.2
  • 40
    • 0039591930 scopus 로고
    • Persistence under relaxed point-dissipativity (with application to an endemic model)
    • H. R. THIEME, Persistence under relaxed point-dissipativity (with application to an endemic model), SIAM J. Math. Anal., 24 (1993), pp. 407-435.
    • (1993) SIAM J. Math. Anal. , vol.24 , pp. 407-435
    • Thieme, H.R.1
  • 41
    • 0035888649 scopus 로고    scopus 로고
    • Permanence and stability of a stage-structured predator-prey model
    • W. WANG, G. MULONE, F. SALEMI, AND V. SALONE, Permanence and stability of a stage-structured predator-prey model, J. Math. Anal. Appl., 262 (2001), pp. 499-528.
    • (2001) J. Math. Anal. Appl. , vol.262 , pp. 499-528
    • Wang, W.1    Mulone, G.2    Salemi, F.3    Salone, V.4


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