Permanence and Exponential Stability of a Predator-prey Model with HV-Holling Functional Response
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Permanence and Exponential Stability of a Predator-prey Model with HV-Holling Functional Response

Authors: Kai Wang, Yanling Zu

Abstract:

In this paper, a delayed predator-prey system with Hassell-Varley-Holling type functional response is studied. A sufficient criterion for the permanence of the system is presented, and further some sufficient conditions for the global attractivity and exponential stability of the system are established. And an example is to show the feasibility of the results by simulation.

Keywords: Predator-prey system, Hassell-Varley-Holling, delay, permanence, exponential stability.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1058659

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[1] A. Lotka, The Elements of Physical Biology, Williams and Wilkins, Baltimore, 1925.
[2] V. Volterra, Variazioni e fluttuazioni del numero di individui in specie animali conviventi, Mem. Accd. Lincei. 2 (1926) 31-113.
[3] Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, New York, 1993.
[4] C. Chen and F.D. Chen, Conditions for global attractivity of multispecies ecological competition-predator system with Holling III type functional response. J. Biomath. 19 (2004) 136-140.
[5] X.Z. He, Stability and delays in a predator-prey system. J. Math. Anal. Appl. 198 (1996) 355-370.
[6] F.D. Chen, Permanence and global stability of nonautonomous Lotka- Volterra system with predator-prey and deviating arguments. Appl. Math. Comput. 173 (2006) 1082-1100.
[7] M. Fan, Global existence of positive periodic solution of predator-prey system with deviating arguments. Acta Math. Appl. Sin. 23 (2000) 557- 561.
[8] J.D. Zhao and W.C. Chen, Global asymptotic stability of a periodic ecological model. Appl. Math. Comput. 147 (2004) 881-892.
[9] F.D. Chen, The permanence and global attractivity of Lotka-Volterra competition system with feedback controls. Nonlinear Anal. Real World Appl. 7 (2006) 133-143.
[10] Y.H. Xia, J.D. Cao and S.S. Cheng, Periodic solutions for a Lotka- Volterra mutualism system with several delays. Appl. Math. Modelling 31 (2007) 1960-1969.
[11] C. Cosner, D.L. DeAngelis, J.S. Ault and D.B. Olson, Effect of spatial grouping on the functional response of predators, Theor. Pop. Biol. 56 (1999) 65-75.
[12] C.S. Holling, The components of predation as revealed by a study of small mammal predation of the European pine sawfly, Canad. Entomological Soc. 91 (1959) 293-320.
[13] C.S. Holling, Some characteristics of simple types of predation and parasitism, Canad. Entomologist 91 (1959) 385-395.
[14] J.R. Beddington, Mutual interference between parasites or predators and its effect on searching efficiency, J. Animal Ecology 44 (1975) 331-341.
[15] D.L. DeAngelis, Goldsten RA and Neill R, A model for trophic interaction, Ecology 56 (1975) 881-892.
[16] P.H. Crowley and E.K. Martin, Functional response and interference within and between year classes of a dragonfly population. J. North American Benthological 8 (1989) 211-21.
[17] M.P. Hassell and G.C. Varley, New inductive population model for insect parasites and its bearing on biological control, Nature 223 (1969) 1133- 1137.
[18] S.-B. Hsu, T.-W. Hwang and Y. Kuang, Global dynamics of a predatorCprey model with Hassell-Varley type functional response, Discrete Contin. Dyn. Syst. Ser. B 10 (2008) 857-871.
[19] K. Wang, Permanence and global asymptotic stability of a delayed predator-prey model with Hassell-Varley type functional response, Bullet. Iranian Math. Soci. 37 (2011) 203-220.
[20] D. Schenk, L. Bersier and S. Bacher, An experimental test of the nature of predation: neither prey- nor ratio-dependent, J. Animal Ecology 74 (2005) 86-91.
[21] X.X. Liu and Y.J. Lou, Global dynamics of a predator-prey model, J. Math. Anal. Appl. 371 (2010) 323-340.