메뉴 건너뛰기




Volumn 13, Issue 6, 2012, Pages 2790-2793

Global asymptotical stability of the positive equilibrium of the Lotka-Volterra prey-predator model incorporating a constant number of prey refuges

Author keywords

Lotka Volterra predator prey systems; Positive equilibrium; Prey refuge

Indexed keywords

GLOBAL ASYMPTOTICAL STABILITY; LOTKA-VOLTERRA; LOTKA-VOLTERRA PREDATOR-PREY SYSTEM; POSITIVE EQUILIBRIUM; PREY-PREDATOR MODELS; PREY-REFUGE; STABILITY PROPERTIES; SUFFICIENT CONDITIONS;

EID: 84861930656     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2012.04.006     Document Type: Article
Times cited : (59)

References (26)
  • 1
    • 11144275393 scopus 로고    scopus 로고
    • Stability analysis of a prey-predator model incorporating a prey refuge
    • T. Kumar Kar Stability analysis of a prey-predator model incorporating a prey refuge Commun. Nonlinear. Sci. Numer. Simul. 10 2005 681 691
    • (2005) Commun. Nonlinear. Sci. Numer. Simul. , vol.10 , pp. 681-691
    • Kumar Kar, T.1
  • 2
    • 24144432087 scopus 로고    scopus 로고
    • Modelling and analysis of a harvested prey-predator system incorporating a prey refuge
    • T. Kumar Kar Modelling and analysis of a harvested prey-predator system incorporating a prey refuge J. Comput. Appl. Math. 185 2006 19 33
    • (2006) J. Comput. Appl. Math. , vol.185 , pp. 19-33
    • Kumar Kar, T.1
  • 3
    • 7444228735 scopus 로고    scopus 로고
    • Influence of prey reserve capacity on predator-prey dynamics
    • P.D.N. Srinivasu, and I.L. Gayatri Influence of prey reserve capacity on predator-prey dynamics Ecol. Model. 181 2005 191 202
    • (2005) Ecol. Model. , vol.181 , pp. 191-202
    • Srinivasu, P.D.N.1    Gayatri, I.L.2
  • 4
    • 33749640702 scopus 로고    scopus 로고
    • Qualitative analysis of a predator-prey model with Holling type II functional response incorporating a prey refuge
    • W. Ko, and K. Ryu Qualitative analysis of a predator-prey model with Holling type II functional response incorporating a prey refuge J. Differential Equations 231 2006 534 550
    • (2006) J. Differential Equations , vol.231 , pp. 534-550
    • Ko, W.1    Ryu, K.2
  • 5
    • 33750824327 scopus 로고    scopus 로고
    • Stability analysis of a prey-predator model with Holling type III response function incorporating a prey refuge
    • Y. Huang, F. Chen, and Z. Li Stability analysis of a prey-predator model with Holling type III response function incorporating a prey refuge Appl. Math. Comput. 182 2006 672 683
    • (2006) Appl. Math. Comput. , vol.182 , pp. 672-683
    • Huang, Y.1    Chen, F.2    Li, Z.3
  • 6
    • 64049105932 scopus 로고    scopus 로고
    • On a Leslie-Gower predator-prey model incorporating a prey refuge
    • F.D. Chen, L.J. Chen, and X.D. Xie On a Leslie-Gower predator-prey model incorporating a prey refuge Nonlinear Anal.: Real World Appl. 10 5 2009 2905 2908
    • (2009) Nonlinear Anal.: Real World Appl. , vol.10 , Issue.5 , pp. 2905-2908
    • Chen, F.D.1    Chen, L.J.2    Xie, X.D.3
  • 7
    • 77956063179 scopus 로고    scopus 로고
    • Effect of prey refuge on a harvested predator-prey model with generalized functional response
    • Y.D. Tao, X. Wang, and X.Y. Song Effect of prey refuge on a harvested predator-prey model with generalized functional response Commun. Nonlinear. Sci. Numer. Simul. 16 2 2011 1052 1059
    • (2011) Commun. Nonlinear. Sci. Numer. Simul. , vol.16 , Issue.2 , pp. 1052-1059
    • Tao, Y.D.1    Wang, X.2    Song, X.Y.3
  • 8
    • 70350716708 scopus 로고    scopus 로고
    • Qualitative analysis of a predator-prey model with Holling type II functional response incorporating a constant prey refuge
    • L.J. Chen, F.D. Chen, and L.J. Chen Qualitative analysis of a predator-prey model with Holling type II functional response incorporating a constant prey refuge Nonlinear Anal.: Real World Appl. 11 1 2010 246 252
    • (2010) Nonlinear Anal.: Real World Appl. , vol.11 , Issue.1 , pp. 246-252
    • Chen, L.J.1    Chen, F.D.2    Chen, L.J.3
  • 9
    • 77955769563 scopus 로고    scopus 로고
    • Qualitative analysis of a predator-prey model with constant-rate prey harvesting incorporating a constant prey refuge
    • L.L. Ji, and C.Q. Wu Qualitative analysis of a predator-prey model with constant-rate prey harvesting incorporating a constant prey refuge Nonlinear Anal.: Real World Appl. 11 4 2010 2285 2295
    • (2010) Nonlinear Anal.: Real World Appl. , vol.11 , Issue.4 , pp. 2285-2295
    • Ji, L.L.1    Wu, C.Q.2
  • 10
    • 62249093792 scopus 로고    scopus 로고
    • Effects of prey refuges on a predator-prey model with a class of functional response: The role of refuges
    • Z.H. Ma, W.L. Li, and Y. Zhao Effects of prey refuges on a predator-prey model with a class of functional response: the role of refuges Math. Biosci. 218 2009 73 79
    • (2009) Math. Biosci. , vol.218 , pp. 73-79
    • Ma, Z.H.1    Li, W.L.2    Zhao, Y.3
  • 12
    • 64949110537 scopus 로고    scopus 로고
    • Modeling inverted biomass pyramids and refuges in ecosystems
    • H. Wang, W. Morrison, A. Singh, and H. Weiss Modeling inverted biomass pyramids and refuges in ecosystems Ecol. Model. 220 2009 1376 1382
    • (2009) Ecol. Model. , vol.220 , pp. 1376-1382
    • Wang, H.1    Morrison, W.2    Singh, A.3    Weiss, H.4
  • 13
    • 78649953589 scopus 로고    scopus 로고
    • Stability analysis of an eco-epidemiological model incorporating a prey refuge
    • A.K. Pal, and G.P. Samanta Stability analysis of an eco-epidemiological model incorporating a prey refuge Nonlinear Anal.: Model. Control 15 4 2010 473 491
    • (2010) Nonlinear Anal.: Model. Control , vol.15 , Issue.4 , pp. 473-491
    • Pal, A.K.1    Samanta, G.P.2
  • 14
    • 68149171904 scopus 로고    scopus 로고
    • Stability results for a class of differential equation and application in medicine
    • Article ID 187021
    • Q.Y. Zhan, X.D. Xie, and Z.F. Zhang Stability results for a class of differential equation and application in medicine Abstr. Appl. Anal. 2009 2009 8 Article ID 187021
    • (2009) Abstr. Appl. Anal. , vol.2009 , pp. 8
    • Zhan, Q.Y.1    Xie, X.D.2    Zhang, Z.F.3
  • 15
    • 0348077455 scopus 로고    scopus 로고
    • Dynamic consequences of prey refuges in a simple model system: More prey, fewer predators and enhanced stability
    • E. González-Olivares, and R. Ramos-Jiliberto Dynamic consequences of prey refuges in a simple model system: more prey, fewer predators and enhanced stability Ecol. Model. 166 2003 135 146
    • (2003) Ecol. Model. , vol.166 , pp. 135-146
    • González-Olivares, E.1    Ramos-Jiliberto, R.2
  • 16
    • 79955523591 scopus 로고    scopus 로고
    • Spatiotemporal dynamics of a Leslie-Gower predator-prey model incorporating a prey refuge
    • X.N. Guan, W.M. Wang, and Y.L. Cai Spatiotemporal dynamics of a Leslie-Gower predator-prey model incorporating a prey refuge Nonlinear Anal.: Real World Appl. 12 4 2011 2385 2395
    • (2011) Nonlinear Anal.: Real World Appl. , vol.12 , Issue.4 , pp. 2385-2395
    • Guan, X.N.1    Wang, W.M.2    Cai, Y.L.3
  • 17
    • 84861923349 scopus 로고    scopus 로고
    • Dynamical behaviors in a discrete predator-prey model with a prey refuge
    • K.J. Zhuang, and Z.H. Wen Dynamical behaviors in a discrete predator-prey model with a prey refuge Int. J. Comput. Numer. Anal. Appl. 5 4 2011 194 197
    • (2011) Int. J. Comput. Numer. Anal. Appl. , vol.5 , Issue.4 , pp. 194-197
    • Zhuang, K.J.1    Wen, Z.H.2
  • 18
    • 79251627743 scopus 로고    scopus 로고
    • Permanence of a discrete model of mutualism with infinite deviating arguments
    • Article ID 931798
    • X.P. Li, and W.S. Yang Permanence of a discrete model of mutualism with infinite deviating arguments Discrete Dyn. Nat. Soc. 2010 2010 7 Article ID 931798
    • (2010) Discrete Dyn. Nat. Soc. , vol.2010 , pp. 7
    • Li, X.P.1    Yang, W.S.2
  • 19
    • 68349105945 scopus 로고    scopus 로고
    • Permanence and global attractivity of discrete predator-prey system with Hassell-Varley type functional response
    • Article ID 323065
    • R.X. Wu, and L. Li Permanence and global attractivity of discrete predator-prey system with Hassell-Varley type functional response Discrete Dyn. Nat. Soc. 2009 2009 17 Article ID 323065
    • (2009) Discrete Dyn. Nat. Soc. , vol.2009 , pp. 17
    • Wu, R.X.1    Li, L.2
  • 20
    • 79952625579 scopus 로고    scopus 로고
    • Stability and instability analysis for a ratio-dependent predator-prey system with diffusion effect
    • M.X. Liao, X.H. Tang, and C.J. Xu Stability and instability analysis for a ratio-dependent predator-prey system with diffusion effect Nonlinear Anal.: Real World Appl. 12 2011 1616 1626
    • (2011) Nonlinear Anal.: Real World Appl. , vol.12 , pp. 1616-1626
    • Liao, M.X.1    Tang, X.H.2    Xu, C.J.3
  • 21
    • 84856393721 scopus 로고    scopus 로고
    • Positive periodic solutions for impulsive Gause-type predator-prey systems
    • X. Ding, B. Su, and J. Hao Positive periodic solutions for impulsive Gause-type predator-prey systems Appl. Math. Comput. 218 2012 6785 6797
    • (2012) Appl. Math. Comput. , vol.218 , pp. 6785-6797
    • Ding, X.1    Su, B.2    Hao, J.3
  • 22
    • 80053638826 scopus 로고    scopus 로고
    • Positive solutions for a general Gause-type predator-prey model with monotonic functional response
    • Art. No. 547060
    • G. Zhang, and X. Wang Positive solutions for a general Gause-type predator-prey model with monotonic functional response Abstr. Appl. Anal. 2011 Art. No. 547060
    • (2011) Abstr. Appl. Anal.
    • Zhang, G.1    Wang, X.2
  • 23
    • 79251592857 scopus 로고    scopus 로고
    • On the Gause predator-prey model with a refuge: A fresh look at the history
    • V. Krivan On the Gause predator-prey model with a refuge: a fresh look at the history J. Theoret. Biol. 274 2011 67 73
    • (2011) J. Theoret. Biol. , vol.274 , pp. 67-73
    • Krivan, V.1
  • 24
    • 80052031437 scopus 로고    scopus 로고
    • Multiple stability and uniqueness of the limit cycle in a Gause-type predator prey model considering the Allee effect on prey
    • E. González-Olivares, H. Meneses-Alcay, and B. González-Yaez Multiple stability and uniqueness of the limit cycle in a Gause-type predator prey model considering the Allee effect on prey Nonlinear Anal.: Real World Appl. 12 2011 2931 2942
    • (2011) Nonlinear Anal.: Real World Appl. , vol.12 , pp. 2931-2942
    • González-Olivares, E.1    Meneses-Alcay, H.2    González-Yaez, B.3
  • 25
    • 78249285621 scopus 로고    scopus 로고
    • Chaos and Hopf bifurcation analysis for a two species predator-prey system with prey refuge and diffusion
    • X. Liu, and M.A. Han Chaos and Hopf bifurcation analysis for a two species predator-prey system with prey refuge and diffusion Nonlinear Anal.: Real World Appl. 12 2011 1047 1061
    • (2011) Nonlinear Anal.: Real World Appl. , vol.12 , pp. 1047-1061
    • Liu, X.1    Han, M.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.