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Volumn 9, Issue 2, 2008, Pages 207-221

Permanence, extinction and periodic solution of the predator-prey system with Beddington-DeAngelis functional response and stage structure for prey

Author keywords

Beddington DeAngelis functional response; Extinction; Periodic solution; Permanence; Predator; Prey; Stage structure

Indexed keywords

COMPUTER SIMULATION; FUNCTIONAL ANALYSIS; NUMERICAL METHODS; PROBLEM SOLVING;

EID: 37249010589     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2006.09.009     Document Type: Article
Times cited : (61)

References (45)
  • 1
    • 0001687872 scopus 로고
    • Analysis of a model representing stage- structure population growth with state-dependent time delay
    • Aiello W.G., Freedman H.I., and Wu J. Analysis of a model representing stage- structure population growth with state-dependent time delay. SIAM J. Appl. Math. 52 (1992) 855-869
    • (1992) SIAM J. Appl. Math. , vol.52 , pp. 855-869
    • Aiello, W.G.1    Freedman, H.I.2    Wu, J.3
  • 2
    • 0000076167 scopus 로고
    • Mutual interference between parasites or predators and its effect on searching efficiency
    • Beddington J.R. Mutual interference between parasites or predators and its effect on searching efficiency. J. Animal. Ecol. 44 (1975) 331-340
    • (1975) J. Animal. Ecol. , vol.44 , pp. 331-340
    • Beddington, J.R.1
  • 3
    • 0024900429 scopus 로고
    • Space-limited recruitment in open system: the importance of time delays
    • Bence J.R., and Nisbet R.M. Space-limited recruitment in open system: the importance of time delays. Ecology 70 (1989) 1434-1441
    • (1989) Ecology , vol.70 , pp. 1434-1441
    • Bence, J.R.1    Nisbet, R.M.2
  • 4
    • 0000927270 scopus 로고    scopus 로고
    • Qualitative behavior of stage-structure populations: application to structural validation
    • Bernard O., and Souissi S. Qualitative behavior of stage-structure populations: application to structural validation. J. Math. Biol. 37 (1998) 291-308
    • (1998) J. Math. Biol. , vol.37 , pp. 291-308
    • Bernard, O.1    Souissi, S.2
  • 5
    • 0027075622 scopus 로고
    • The origins and evolution of predator-prey theory
    • Berryman A.A. The origins and evolution of predator-prey theory. Ecology 75 (1992) 1530-1535
    • (1992) Ecology , vol.75 , pp. 1530-1535
    • Berryman, A.A.1
  • 6
    • 0038750243 scopus 로고    scopus 로고
    • On the dynamics of predator-prey models with the Beddington-DeAngelis functional response
    • Cantrell R.S., and Cosner C. On the dynamics of predator-prey models with the Beddington-DeAngelis functional response. J. Math. Anal. Appl. 25 1 (2001) 206-222
    • (2001) J. Math. Anal. Appl. , vol.25 , Issue.1 , pp. 206-222
    • Cantrell, R.S.1    Cosner, C.2
  • 7
    • 27144519729 scopus 로고    scopus 로고
    • Periodic solutions of a delayed predator-prey model with stage structure for predator
    • Chen F.D. Periodic solutions of a delayed predator-prey model with stage structure for predator. J. Appl. Math. 2005 2 (2005) 153-169
    • (2005) J. Appl. Math. , vol.2005 , Issue.2 , pp. 153-169
    • Chen, F.D.1
  • 8
    • 17644427702 scopus 로고    scopus 로고
    • On a nonlinear non-autonomous predator-prey model with diffusion and distributed delay
    • Chen F.D. On a nonlinear non-autonomous predator-prey model with diffusion and distributed delay. J. Comput. Appl. Math. 180 1 (2005) 33-49
    • (2005) J. Comput. Appl. Math. , vol.180 , Issue.1 , pp. 33-49
    • Chen, F.D.1
  • 9
    • 28444438091 scopus 로고    scopus 로고
    • On a periodic multi-species ecological model
    • Chen F.D. On a periodic multi-species ecological model. Appl. Math. Comput. 171 1 (2005) 492-510
    • (2005) Appl. Math. Comput. , vol.171 , Issue.1 , pp. 492-510
    • Chen, F.D.1
  • 10
    • 12244274373 scopus 로고    scopus 로고
    • Positive periodic solutions of neutral Lotka-Volterra system with feedback control
    • Chen F.D. Positive periodic solutions of neutral Lotka-Volterra system with feedback control. Appl. Math. Comput. 162 3 (2005) 1279-1302
    • (2005) Appl. Math. Comput. , vol.162 , Issue.3 , pp. 1279-1302
    • Chen, F.D.1
  • 11
    • 33745167944 scopus 로고    scopus 로고
    • Some new results on the permanence and extinction of nonautonomous Gilpin-Ayala type competition model with delays
    • Chen F.D. Some new results on the permanence and extinction of nonautonomous Gilpin-Ayala type competition model with delays. Nonlinear Anal. Real World Appl. 7 5 (2006) 1205-1222
    • (2006) Nonlinear Anal. Real World Appl. , vol.7 , Issue.5 , pp. 1205-1222
    • Chen, F.D.1
  • 12
    • 30344439489 scopus 로고    scopus 로고
    • Dynamic behavior of a nonlinear single species diffusive system
    • Chen F.D., Chen X.X., and Shi J.L. Dynamic behavior of a nonlinear single species diffusive system. Adv. Complex Systems 8 4 (2005) 399-417
    • (2005) Adv. Complex Systems , vol.8 , Issue.4 , pp. 399-417
    • Chen, F.D.1    Chen, X.X.2    Shi, J.L.3
  • 13
    • 9744231393 scopus 로고    scopus 로고
    • Periodicity in a Logistic type system with several delays
    • Chen F.D., and Shi J.L. Periodicity in a Logistic type system with several delays. Comput. Math. Appl. 48 1-2 (2004) 35-44
    • (2004) Comput. Math. Appl. , vol.48 , Issue.1-2 , pp. 35-44
    • Chen, F.D.1    Shi, J.L.2
  • 14
    • 0346903415 scopus 로고    scopus 로고
    • Periodicity in a food-limited population model with toxicants and state dependent delays
    • Chen F.D., Sun D.X., and Shi J.L. Periodicity in a food-limited population model with toxicants and state dependent delays. J. Math. Anal. Appl. 288 1 (2003) 136-146
    • (2003) J. Math. Anal. Appl. , vol.288 , Issue.1 , pp. 136-146
    • Chen, F.D.1    Sun, D.X.2    Shi, J.L.3
  • 15
    • 26844511430 scopus 로고    scopus 로고
    • Qualitative analysis of predator-prey models with Beddington-DeAngelis functional response and diffusion
    • Chen W., and Wang M.X. Qualitative analysis of predator-prey models with Beddington-DeAngelis functional response and diffusion. Math. Comput. Modelling 42 1-2 (2005) 31-44
    • (2005) Math. Comput. Modelling , vol.42 , Issue.1-2 , pp. 31-44
    • Chen, W.1    Wang, M.X.2
  • 16
    • 28844486610 scopus 로고    scopus 로고
    • Dispersal permanence of a periodic predator-prey system with Beddington-DeAngelis functional response
    • Cui J.A. Dispersal permanence of a periodic predator-prey system with Beddington-DeAngelis functional response. Nonlinear Anal. 64 3 (2006) 440-456
    • (2006) Nonlinear Anal. , vol.64 , Issue.3 , pp. 440-456
    • Cui, J.A.1
  • 17
    • 0012099291 scopus 로고    scopus 로고
    • The effect of dispersal on population growth with stage-structure
    • Cui J., Chen L., and Wang W. The effect of dispersal on population growth with stage-structure. Computers Math. Appl. 39 (2000) 91-102
    • (2000) Computers Math. Appl. , vol.39 , pp. 91-102
    • Cui, J.1    Chen, L.2    Wang, W.3
  • 18
    • 2942655606 scopus 로고    scopus 로고
    • Permanence of a predator-prey system with stage structure
    • Cui J.A., and Song X.Y. Permanence of a predator-prey system with stage structure. Discrete Continuous Dynam. Systems Ser. B 4 3 (2004) 547-554
    • (2004) Discrete Continuous Dynam. Systems Ser. B , vol.4 , Issue.3 , pp. 547-554
    • Cui, J.A.1    Song, X.Y.2
  • 19
    • 33644590203 scopus 로고    scopus 로고
    • Permanence, extinction and periodic solution of predator-prey system with Beddington-DeAngelis functional response
    • Cui J.A., and Takeuchi Y. Permanence, extinction and periodic solution of predator-prey system with Beddington-DeAngelis functional response. J. Math. Anal. Appl. 317 2 (2006) 464-474
    • (2006) J. Math. Anal. Appl. , vol.317 , Issue.2 , pp. 464-474
    • Cui, J.A.1    Takeuchi, Y.2
  • 21
    • 10444225454 scopus 로고    scopus 로고
    • Complete mathematical analysis of predator-prey models with linear prey growth and Beddington-DeAngelis functional response
    • Dimitrov D.T., and Kojouharov H.V. Complete mathematical analysis of predator-prey models with linear prey growth and Beddington-DeAngelis functional response. Appl. Math. Comput. 162 2 (2005) 523-538
    • (2005) Appl. Math. Comput. , vol.162 , Issue.2 , pp. 523-538
    • Dimitrov, D.T.1    Kojouharov, H.V.2
  • 22
    • 2942641510 scopus 로고    scopus 로고
    • Dynamics of a nonautonomous predator-prey system with the Beddington-DeAngelis functional response
    • Fan M., and Kuang Y. Dynamics of a nonautonomous predator-prey system with the Beddington-DeAngelis functional response. J. Math. Anal. Appl. 295 1 (2004) 15-39
    • (2004) J. Math. Anal. Appl. , vol.295 , Issue.1 , pp. 15-39
    • Fan, M.1    Kuang, Y.2
  • 23
    • 37249081462 scopus 로고    scopus 로고
    • H.F. Huo, W.T. Li, J.J. Nieto, Periodic solutions of delayed predator-prey model with the Beddington-DeAngelis functional response, Chaos, Solitons and Fractals, in press.
  • 24
    • 0037670816 scopus 로고    scopus 로고
    • Global analysis of the predator-prey system with Beddington-DeAngelis functional response
    • Hwang T.W. Global analysis of the predator-prey system with Beddington-DeAngelis functional response. J. Math. Anal. Appl. 281 1 (2003) 395-401
    • (2003) J. Math. Anal. Appl. , vol.281 , Issue.1 , pp. 395-401
    • Hwang, T.W.1
  • 25
    • 1242344859 scopus 로고    scopus 로고
    • Uniqueness of limit cycles of the predator-prey system with Beddington-DeAngelis functional response
    • Hwang T.W. Uniqueness of limit cycles of the predator-prey system with Beddington-DeAngelis functional response. J. Math. Anal. Appl. 290 1 (2004) 113-122
    • (2004) J. Math. Anal. Appl. , vol.290 , Issue.1 , pp. 113-122
    • Hwang, T.W.1
  • 26
    • 33845634818 scopus 로고    scopus 로고
    • T.K. Kar, U.K. Pahari, Modelling and analysis of a prey-predator system with stage-structure and harvesting, Nonlinear Analysis: Real World Appl., in press, doi:10.1016/j.nonrwa.2006.01.004.
  • 27
    • 33645868969 scopus 로고    scopus 로고
    • The dynamics of a Beddington-type system with impulsive control strategy
    • Li Z.Q., Wang W.M., and Wang H.L. The dynamics of a Beddington-type system with impulsive control strategy. Chaos, Solitons and Fractals 29 5 (2006) 1229-1239
    • (2006) Chaos, Solitons and Fractals , vol.29 , Issue.5 , pp. 1229-1239
    • Li, Z.Q.1    Wang, W.M.2    Wang, H.L.3
  • 28
    • 0037110188 scopus 로고    scopus 로고
    • Extinction and permanence in nonautonomous competitive system with stage structure
    • Liu S.Q., Chen L.S., and Liu Z.J. Extinction and permanence in nonautonomous competitive system with stage structure. J. Math. Anal. Appl. 274 2 (2002) 667-684
    • (2002) J. Math. Anal. Appl. , vol.274 , Issue.2 , pp. 667-684
    • Liu, S.Q.1    Chen, L.S.2    Liu, Z.J.3
  • 29
    • 0036883834 scopus 로고    scopus 로고
    • Extinction and permanence in competitive stage structured system with time-delays
    • Liu S.Q., Chen L.S., and Luo G.L. Extinction and permanence in competitive stage structured system with time-delays. Nonlinear Anal. 51 8 (2002) 1347-1361
    • (2002) Nonlinear Anal. , vol.51 , Issue.8 , pp. 1347-1361
    • Liu, S.Q.1    Chen, L.S.2    Luo, G.L.3
  • 30
    • 3442890192 scopus 로고    scopus 로고
    • Stability and bifurcation in a delayed predator-prey system with Beddington-DeAngelis functional response
    • Liu Z.H., and Yuan R. Stability and bifurcation in a delayed predator-prey system with Beddington-DeAngelis functional response. J. Math. Anal. Appl. 296 2 (2004) 521-537
    • (2004) J. Math. Anal. Appl. , vol.296 , Issue.2 , pp. 521-537
    • Liu, Z.H.1    Yuan, R.2
  • 31
    • 37249013802 scopus 로고    scopus 로고
    • R.K. Naji, A.T. Balasim, Dynamical behavior of a three species food chain model with Beddington-DeAngelis functional response, Chaos, Solitons and Fractals, in press.
  • 32
    • 0346671147 scopus 로고    scopus 로고
    • The asymptotic behavior of a chemostat model with the Beddington-DeAngelis functional response
    • Qui Z.P., Yu J., and Zou Y. The asymptotic behavior of a chemostat model with the Beddington-DeAngelis functional response. Math. Biosci. 187 2 (2004) 175-187
    • (2004) Math. Biosci. , vol.187 , Issue.2 , pp. 175-187
    • Qui, Z.P.1    Yu, J.2    Zou, Y.3
  • 33
    • 0006419374 scopus 로고    scopus 로고
    • The positive periodic solutions in periodic Kolmogorov type systems with delays (in Chinese)
    • Teng Z., and Chen L. The positive periodic solutions in periodic Kolmogorov type systems with delays (in Chinese). Acta Math. Appl. Sinica, 22 (1999) 446-456
    • (1999) Acta Math. Appl. Sinica , vol.22 , pp. 446-456
    • Teng, Z.1    Chen, L.2
  • 34
    • 0035888649 scopus 로고    scopus 로고
    • Permanence and stability of a stage-structured predator-prey model
    • Wang W., Mulone G., Salemi F., and Salone V. Permanence and stability of a stage-structured predator-prey model. J. Math. Anal. Appl. 262 2 (2001) 499-528
    • (2001) J. Math. Anal. Appl. , vol.262 , Issue.2 , pp. 499-528
    • Wang, W.1    Mulone, G.2    Salemi, F.3    Salone, V.4
  • 35
    • 31144452709 scopus 로고    scopus 로고
    • Asymptotic behavior of solutions in nonautonomous predator-prey patchy system with beddington-type functional response
    • Wang H.L., and Zhong S.M. Asymptotic behavior of solutions in nonautonomous predator-prey patchy system with beddington-type functional response. Appl. Math. Comput. 172 1 (2006) 122-140
    • (2006) Appl. Math. Comput. , vol.172 , Issue.1 , pp. 122-140
    • Wang, H.L.1    Zhong, S.M.2
  • 36
    • 37249086075 scopus 로고    scopus 로고
    • Y. Xiao, Study on the eco-epidemiology dynamical system, Ph.D. Thesis, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, 2001.
  • 37
    • 13844265911 scopus 로고    scopus 로고
    • Permanence and periodicity of a delayed ratio-dependent predator-prey model with stage structure
    • Xu R., Chaplain M.A.J., and Davidson F.A. Permanence and periodicity of a delayed ratio-dependent predator-prey model with stage structure. J. Math. Anal. Appl. 303 2 (2005) 602-621
    • (2005) J. Math. Anal. Appl. , vol.303 , Issue.2 , pp. 602-621
    • Xu, R.1    Chaplain, M.A.J.2    Davidson, F.A.3
  • 38
    • 29544450162 scopus 로고    scopus 로고
    • A Lotka-Volterra type food chain model with stage structure and time delays
    • Xu R., Chaplain M.A.J., and Davidson F.A. A Lotka-Volterra type food chain model with stage structure and time delays. J. Math. Anal. Appl. 315 1 (2006) 90-105
    • (2006) J. Math. Anal. Appl. , vol.315 , Issue.1 , pp. 90-105
    • Xu, R.1    Chaplain, M.A.J.2    Davidson, F.A.3
  • 39
    • 10644274227 scopus 로고    scopus 로고
    • Periodic solutions of a predator-prey system with stage-structures for predator and prey
    • Zhang Z.Q. Periodic solutions of a predator-prey system with stage-structures for predator and prey. J. Math. Anal. Appl. 302 2 (2005) 291-305
    • (2005) J. Math. Anal. Appl. , vol.302 , Issue.2 , pp. 291-305
    • Zhang, Z.Q.1
  • 40
    • 22344452897 scopus 로고    scopus 로고
    • A study of predator-prey models with the Beddington-DeAnglis functional response and impulsive effect
    • Zhang S.W., and Chen L.S. A study of predator-prey models with the Beddington-DeAnglis functional response and impulsive effect. Chaos, Solitons and Fractals 27 1 (2006) 237-248
    • (2006) Chaos, Solitons and Fractals , vol.27 , Issue.1 , pp. 237-248
    • Zhang, S.W.1    Chen, L.S.2
  • 41
    • 2942669677 scopus 로고    scopus 로고
    • The stage-structured predator-prey model and optimal harvesting policy
    • Zhang X., Chen L., and Neumann A.U. The stage-structured predator-prey model and optimal harvesting policy. Math. Biosci. 101 (2000) 139-153
    • (2000) Math. Biosci. , vol.101 , pp. 139-153
    • Zhang, X.1    Chen, L.2    Neumann, A.U.3
  • 42
    • 31444451666 scopus 로고    scopus 로고
    • Chaotic behavior of a chemostat model with Beddington-DeAngelis functional response and periodically impulsive invasion
    • Zhang S.W., Tan D.J., and Chen L.S. Chaotic behavior of a chemostat model with Beddington-DeAngelis functional response and periodically impulsive invasion. Chaos, Solitons and Fractals 29 2 (2006) 474-482
    • (2006) Chaos, Solitons and Fractals , vol.29 , Issue.2 , pp. 474-482
    • Zhang, S.W.1    Tan, D.J.2    Chen, L.S.3
  • 43
    • 23144449908 scopus 로고    scopus 로고
    • Dynamic complexities of a food chain model with impulsive perturbations and Beddington-DeAngelis functional response
    • Zhang S.W., Tan D.J., and Chen L.S. Dynamic complexities of a food chain model with impulsive perturbations and Beddington-DeAngelis functional response. Chaos, Solitons and Fractals 27 3 (2006) 768-777
    • (2006) Chaos, Solitons and Fractals , vol.27 , Issue.3 , pp. 768-777
    • Zhang, S.W.1    Tan, D.J.2    Chen, L.S.3
  • 44
    • 1842832866 scopus 로고    scopus 로고
    • Periodic solutions of nonautonomous stage-structured cooperative system
    • Zhang Z.Q., Wu J., and Wang Z.C. Periodic solutions of nonautonomous stage-structured cooperative system. Comput. Math. Appl. 47 4-5 (2004) 699-706
    • (2004) Comput. Math. Appl. , vol.47 , Issue.4-5 , pp. 699-706
    • Zhang, Z.Q.1    Wu, J.2    Wang, Z.C.3
  • 45
    • 0002943884 scopus 로고
    • The qualitative analysis of N-species Lotka-Volterra periodic competition systems
    • Zhao X.Q. The qualitative analysis of N-species Lotka-Volterra periodic competition systems. Math. Comput. Modeling 15 (1991) 3-8
    • (1991) Math. Comput. Modeling , vol.15 , pp. 3-8
    • Zhao, X.Q.1


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