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Volumn 58, Issue 1-2, 2009, Pages 443-451

The study of a ratio-dependent predator-prey model with stage structure in the prey

Author keywords

Impulsive; Permanent; Predator prey; Prey eradication periodic solution; Ratio dependent; Stage structure

Indexed keywords

IMPULSIVE; PERMANENT; PREDATOR-PREY; PREY-ERADICATION PERIODIC SOLUTION; RATIO-DEPENDENT; STAGE STRUCTURE;

EID: 70349202857     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-009-9491-2     Document Type: Article
Times cited : (39)

References (31)
  • 1
    • 0027100815 scopus 로고
    • Empirical evidence of the role of heterogeneity in ratio-dependent consumption
    • 10.2307/1940007
    • R. Arditi H. Saiah 1992 Empirical evidence of the role of heterogeneity in ratio-dependent consumption Ecology 73 1544 1551 10.2307/1940007
    • (1992) Ecology , vol.73 , pp. 1544-1551
    • Arditi, R.1    Saiah, H.2
  • 2
    • 0000542895 scopus 로고
    • Variation in plankton densities among lakes: A case for ratio-dependent models
    • 10.1086/285286
    • R. Arditi L.R. Ginzburg H.R. Akcakaya 1991 Variation in plankton densities among lakes: A case for ratio-dependent models Am. Nat. 138 1287 1296 10.1086/285286
    • (1991) Am. Nat. , vol.138 , pp. 1287-1296
    • Arditi, R.1    Ginzburg, L.R.2    Akcakaya, H.R.3
  • 3
    • 0027084787 scopus 로고
    • The physiological basis of ratio-dependent predator-prey theory: A metabolic pool model of Nicholson's blowflies as an example
    • 10.2307/1940008
    • A.P. Gutierrez 1992 The physiological basis of ratio-dependent predator-prey theory: A metabolic pool model of Nicholson's blowflies as an example Ecology 73 1552 1563 10.2307/1940008
    • (1992) Ecology , vol.73 , pp. 1552-1563
    • Gutierrez, A.P.1
  • 4
    • 4944258042 scopus 로고
    • Coupling in predator-prey dynamics: Ratio-dependence
    • 10.1016/S0022-5193(89)80211-5
    • R. Arditi L.R. Ginzburg 1989 Coupling in predator-prey dynamics: ratio-dependence J. Theor. Biol. 139 311 326 10.1016/S0022-5193(89)80211-5
    • (1989) J. Theor. Biol. , vol.139 , pp. 311-326
    • Arditi, R.1    Ginzburg, L.R.2
  • 5
    • 0001397558 scopus 로고
    • The functional response of predator: Worries about scale
    • 10.1016/0169-5347(91)90052-Y
    • I. Hanski 1991 The functional response of predator: Worries about scale Trends Ecol. Evol. 6 141 142 10.1016/0169-5347(91)90052-Y
    • (1991) Trends Ecol. Evol. , vol.6 , pp. 141-142
    • Hanski, I.1
  • 6
    • 42949151487 scopus 로고    scopus 로고
    • Multiple periodic solutions in delayed Gause-type ratio-dependent predator-prey systems with non-monotonic numerical responses
    • DOI 10.1016/j.mcm.2007.06.025, PII S0895717707002622
    • X.Q. Ding J.F. Jiang 2008 Multiple periodic solutions in delayed Gause-type ratio-dependent predator-prey systems with non-monotonic numerical responses Math. Comput. Model. 47 1323 1331 1145.34332 10.1016/j.mcm.2007.06.025 2428332 (Pubitemid 351615176)
    • (2008) Mathematical and Computer Modelling , vol.47 , Issue.11-12 , pp. 1323-1331
    • Ding, X.1    Jiang, J.2
  • 7
    • 2942685814 scopus 로고    scopus 로고
    • Ratio-dependent predator-prey system with stage structure for prey
    • Advances in Mathematical Biology
    • X. Song L. Cai A.U. Neumann 2004 Ratio-dependent predator-prey system with stage structure for prey Discrete Continuous Dyn. Syst. Ser. B 4 3 747 758 1114.92056 10.3934/dcdsb.2004.4.747 2073981 (Pubitemid 38782431)
    • (2004) Discrete and Continuous Dynamical Systems - Series B , vol.4 , Issue.3 , pp. 747-758
    • Song, X.1    Cai, L.2    Neumann, A.U.3
  • 8
    • 4944222203 scopus 로고    scopus 로고
    • Persistence and global stability of a ratio-dependent predator-prey model with stage structure
    • 1058.92053 10.1016/j.amc.2003.10.012 2095699
    • R. Xu M.A.J. Chaplain F.A. Davidson 2004 Persistence and global stability of a ratio-dependent predator-prey model with stage structure Appl. Math. Comput. 158 729 744 1058.92053 10.1016/j.amc.2003.10.012 2095699
    • (2004) Appl. Math. Comput. , vol.158 , pp. 729-744
    • Xu, R.1    Chaplain, M.A.J.2    Davidson, F.A.3
  • 9
    • 61549100195 scopus 로고    scopus 로고
    • Numerical solutions of a Michaelis-Menten type ratio-dependent predator-prey system with diffusion
    • 1158.92047 10.1016/j.apnum.2008.05.003 2495139
    • Y.M. Wang 2009 Numerical solutions of a Michaelis-Menten type ratio-dependent predator-prey system with diffusion Appl. Numer. Math. 59 5 1075 1093 1158.92047 10.1016/j.apnum.2008.05.003 2495139
    • (2009) Appl. Numer. Math. , vol.59 , Issue.5 , pp. 1075-1093
    • Wang, Y.M.1
  • 10
    • 43049146573 scopus 로고    scopus 로고
    • Stability and Hopf bifurcation in a ratio-dependent predator-prey system with stage structure
    • DOI 10.1016/j.chaos.2007.01.019, PII S0960077907000203
    • R. Xu Z. Ma 2008 Stability and Hopf bifurcation in a ratio-dependent predator-prey system with stage structure Chaos Solitons Fractals 38 669 684 1146.34323 10.1016/j.chaos.2007.01.019 2423358 (Pubitemid 351633018)
    • (2008) Chaos, Solitons and Fractals , vol.38 , Issue.3 , pp. 669-684
    • Xu, R.1    Ma, Z.2
  • 11
    • 42649125274 scopus 로고    scopus 로고
    • Qualitative behavior of n-dimensional ratio-dependent predator-prey systems
    • 05286421 10.1016/j.amc.2007.10.019 2420582
    • K. Kiss S. Kovács 2008 Qualitative behavior of n-dimensional ratio-dependent predator-prey systems Appl. Math. Comput. 199 535 546 05286421 10.1016/j.amc.2007.10.019 2420582
    • (2008) Appl. Math. Comput. , vol.199 , pp. 535-546
    • Kiss, K.1    Kovács, S.2
  • 12
    • 0037174269 scopus 로고    scopus 로고
    • A ratio-dependent predator-prey model with disease in the prey
    • DOI 10.1016/S0096-3003(01)00156-4, PII S0096300301001564
    • Y.N. Xiao L.S. Chen 2002 A ratio-dependent predator-prey model with disease in the prey Appl. Math. Comput. 131 397 414 1024.92017 10.1016/S0096-3003(01)00156-4 1920234 (Pubitemid 34813494)
    • (2002) Applied Mathematics and Computation , vol.131 , Issue.2-3 , pp. 397-414
    • Xiao, Y.1    Chen, L.2
  • 13
    • 0003421351 scopus 로고
    • V. Lakshmikantham D.D. Bainov P. Simeonov (eds). World Scientific Singapore 0719.34002
    • Lakshmikantham, V., Bainov, D.D., Simeonov, P. (eds.): Theory of Impulsive Differential Equations. World Scientific, Singapore (1989)
    • (1989) Theory of Impulsive Differential Equations
  • 14
    • 0342759064 scopus 로고
    • Impulsive Differential Equations: Periodic Solutions and Applications
    • D. Bainov P. Simeonov (eds). Pitman London 0815.34001
    • Bainov, D., Simeonov, P. (eds.): Impulsive Differential Equations: Periodic Solutions and Applications. Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 66. Pitman, London (1993)
    • (1993) Pitman Monographs and Surveys in Pure and Applied Mathematics , vol.66
  • 16
    • 36949038244 scopus 로고    scopus 로고
    • Permanence and periodic solution of predator-prey system with Holling type functional response and impulses
    • Wang, W., Shen, J., Nieto, J.: Permanence and periodic solution of predator-prey system with Holling type functional response and impulses. Discrete Dyn. Nat. Soc. 2007, Article ID 81756 (2007), 15 pp.
    • (2007) Discrete Dyn. Nat. Soc. 2007, Article ID 81756 , pp. 15
    • Wang, W.1    Shen, J.2    Nieto, J.3
  • 17
    • 43649101953 scopus 로고    scopus 로고
    • A delayed epidemic model with stage-structure and pulses for pest management strategy
    • DOI 10.1016/j.nonrwa.2007.05.004, PII S1468121807000934
    • H. Zhang L. Chen J. Nieto 2008 A delayed epidemic model with stage-structure and pulses for pest management strategy Nonlinear Anal. Real World Appl. 9 4 1714 1726 1154.34394 10.1016/j.nonrwa.2007.05.004 2422575 (Pubitemid 351685810)
    • (2008) Nonlinear Analysis: Real World Applications , vol.9 , Issue.4 , pp. 1714-1726
    • Zhang, H.1    Chen, L.2    Nieto, J.J.3
  • 18
    • 34249790143 scopus 로고    scopus 로고
    • Pest regulation by means of impulsive controls
    • DOI 10.1016/j.amc.2007.01.079, PII S0096300307001130
    • P. Georgescu G. Morosanu 2007 Pest regulation by means of impulsive controls Appl. Math. Comput. 190 790 803 1117.93006 10.1016/j.amc.2007.01.079 2338755 (Pubitemid 46856705)
    • (2007) Applied Mathematics and Computation , vol.190 , Issue.1 , pp. 790-803
    • Georgescu, P.1    Morosanu, G.2
  • 20
    • 50249100273 scopus 로고    scopus 로고
    • Staged-structured Lotka-Volterra predator-prey models for pest management
    • 1152.92029 10.1016/j.amc.2008.04.032 2452283
    • R.Q. Shi L.S. Chen 2008 Staged-structured Lotka-Volterra predator-prey models for pest management Appl. Math. Comput. 203 258 265 1152.92029 10.1016/j.amc.2008.04.032 2452283
    • (2008) Appl. Math. Comput. , vol.203 , pp. 258-265
    • Shi, R.Q.1    Chen, L.S.2
  • 21
    • 0025132577 scopus 로고
    • A time-delay model of single-species growth with stage structure
    • DOI 10.1016/0025-5564(90)90019-U
    • W.G. Aiello H.I. Freedman 1990 A time delay model of single-species growth with stage structure Math. Biosci. 101 139 153 0719.92017 10.1016/0025-5564(90)90019-U 1071716 (Pubitemid 20357965)
    • (1990) Mathematical Biosciences , vol.101 , Issue.2 , pp. 139-153
    • Aiello, W.G.1    Freedman, H.I.2
  • 22
    • 0001687872 scopus 로고
    • Analysis of a model representing stage structured population growth with state-dependent time delay
    • 0760.92018 10.1137/0152048 1163810
    • W.G. Aiello H.I. Freedman J. Wu 1992 Analysis of a model representing stage structured population growth with state-dependent time delay SIAM J. Appl. Math. 52 855 869 0760.92018 10.1137/0152048 1163810
    • (1992) SIAM J. Appl. Math. , vol.52 , pp. 855-869
    • Aiello, W.G.1    Freedman, H.I.2    Wu, J.3
  • 23
    • 0037008798 scopus 로고    scopus 로고
    • Modelling and analysis of a single-species system with stage structure and harvesting
    • DOI 10.1016/S0895-7177(02)00104-8, PII S0895717702001048
    • X.Y. Song L.S. Chen 2002 Modelling and analysis of a single-species system with stage structure and harvesting Math. Comput. Model. 36 67 82 1024.92015 10.1016/S0895-7177(02)00104-8 1925059 (Pubitemid 35044898)
    • (2002) Mathematical and Computer Modelling , vol.36 , Issue.1-2 , pp. 67-82
    • Song, X.1    Chen, L.2
  • 24
    • 2942649902 scopus 로고    scopus 로고
    • Optimal harvesting and stability for a predator-prey system with stage structure
    • 1054.34125 10.1007/s102550200042 2010921
    • X.Y. Song L.S. Chen 2002 Optimal harvesting and stability for a predator-prey system with stage structure Acta Math. Appl. Sin. 18 423 430 1054.34125 10.1007/s102550200042 2010921
    • (2002) Acta Math. Appl. Sin. , vol.18 , pp. 423-430
    • Song, X.Y.1    Chen, L.S.2
  • 25
    • 0031124171 scopus 로고    scopus 로고
    • A predator-prey system with stage-structure for predator
    • 10.1016/S0898-1221(97)00056-4
    • W.D. Wang L.S. Chen 1997 A predator-prey system with stage-structure for predator Comput. Math. Appl. 33 83 91 10.1016/S0898-1221(97)00056-4
    • (1997) Comput. Math. Appl. , vol.33 , pp. 83-91
    • Wang, W.D.1    Chen, L.S.2
  • 26
    • 0037110188 scopus 로고    scopus 로고
    • Extinction and permanence in nonautonomous competitive system with stage structure
    • DOI 10.1016/S0022-247X(02)00329-3, PII S0022247X02003293
    • S.Q. Liu L.S. Chen Z.J. Liu 2002 Extinction and permanence in nonautonomous competitive system with stage structure J. Math. Anal. Appl. 274 667 684 1039.34068 10.1016/S0022-247X(02)00329-3 1936723 (Pubitemid 36006126)
    • (2002) Journal of Mathematical Analysis and Applications , vol.274 , Issue.2 , pp. 667-684
    • Liu, S.1    Chen, L.2    Liu, Z.3
  • 27
    • 33749518760 scopus 로고    scopus 로고
    • Stabilizing effect of cannibalism on a structured competitive system
    • 1041.34033 1903073 (In Chinese)
    • Y.N. Xiao L.S. Chen 2002 Stabilizing effect of cannibalism on a structured competitive system Acta Math. A 22 2 210 216 1041.34033 1903073 (In Chinese)
    • (2002) Acta Math. A , vol.22 , Issue.2 , pp. 210-216
    • Xiao, Y.N.1    Chen, L.S.2
  • 28
    • 0035051672 scopus 로고    scopus 로고
    • Optimal harvesting and stability for a two-species competitive system with stage structure
    • DOI 10.1016/S0025-5564(00)00068-7, PII S0025556400000687
    • X.Y. Song L.S. Chen 2001 Optimal harvesting and stability for a two-species competitive system with stage structure Math. Biosci. 170 2 173 186 1028.34049 10.1016/S0025-5564(00)00068-7 1832710 (Pubitemid 32303991)
    • (2001) Mathematical Biosciences , vol.170 , Issue.2 , pp. 173-186
    • Song, X.1    Chen, L.2
  • 29
    • 33845786533 scopus 로고    scopus 로고
    • An SIS epidemic models with stage structure and a delay
    • 1035.34054 10.1007/s102550200063 2012324
    • Y.N. Xiao L.S. Chen 2002 An SIS epidemic models with stage structure and a delay Acta Math. Appl. Sin., Engl. Ser. 18 4 607 618 1035.34054 10.1007/s102550200063 2012324
    • (2002) Acta Math. Appl. Sin., Engl. Ser. , vol.18 , Issue.4 , pp. 607-618
    • Xiao, Y.N.1    Chen, L.S.2
  • 30
    • 18844445497 scopus 로고    scopus 로고
    • On an SIS epidemic model with stage structure
    • 1138.92369 1979582
    • Y.N. Xiao L.S. Chen 2003 On an SIS epidemic model with stage structure J. Syst. Sci. Complex. 16 275 288 1138.92369 1979582
    • (2003) J. Syst. Sci. Complex. , vol.16 , pp. 275-288
    • Xiao, Y.N.1    Chen, L.S.2
  • 31
    • 0142243570 scopus 로고    scopus 로고
    • Dynamical behavior for a stage-structured SIR infectious disease model
    • DOI 10.1016/S1468-1218(01)00021-9, PII S1468121801000219
    • Y.N. Xiao L.S. Chen F.V.D. Bosh 2002 Dynamical behavior for stage-structured SIR infectious disease model Nonlinear Anal. Real World Appl. 3 175 190 1007.92032 10.1016/S1468-1218(01)00021-9 1893972 (Pubitemid 40030723)
    • (2002) Nonlinear Analysis: Real World Applications , vol.3 , Issue.2 , pp. 175-190
    • Xiao, Y.1    Chen, L.2    Ven Den Bosch, F.3


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