Permanence of Periodic Predator-Prey System with Functional Responses and Stage Structure for Prey

Permanence of Periodic Predator-Prey System with Functional Responses and Stage Structure for Prey

Can-Yun Huang, Min Zhao, and Hai-Feng Huo

Source: Abstr. Appl. Anal. Volume 2008 (2008), 15 pages.

Abstract

A stage-structured three-species predator-prey model with Beddington-DeAngelis and Holling II functional response is introduced. Based on the comparison theorem, sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained. An example is also presented to illustrate our main results.

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aaa/1234298994
Digital Object Identifier: doi:10.1155/2008/371632
Mathematical Reviews number (MathSciNet): MR2453143
Zentralblatt MATH identifier: 05534774

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References

J. R. Beddington, ``Mutual interference between parasites or predators and its effect on searching efficiency,'' The Journal of Animal Ecology, vol. 44, no. 1, pp. 331--340, 1975.

D. L. DeAngelis, R. A. Goldstein, and R. V. O'Neill, ``A model for trophic interaction,'' Ecology, vol. 56, no. 4, pp. 881--892, 1975.

J. Cui and X. Song, ``Permanence of predator-prey system with stage structure,'' Discrete and Continuous Dynamical Systems. Series B, vol. 4, no. 3, pp. 547--554, 2004.

Mathematical Reviews (MathSciNet): MR2073958

Zentralblatt MATH: 1100.92062

Digital Object Identifier: doi:10.3934/dcdsb.2004.4.547

F. D. Chen, ``Periodic solutions of a delayed predator-prey model with stage structure for predator,'' Journal of Applied Mathematics, vol. 2005, no. 2, pp. 153--169, 2005.

R. Xu, M. A. J. Chaplain, and F. A. Davidson, ``A Lotka-Volterra type food chain model with stage structure and time delays,'' Journal of Mathematical Analysis and Applications, vol. 315, no. 1, pp. 90--105, 2006.

Mathematical Reviews (MathSciNet): MR2196532

Zentralblatt MATH: 1096.34055

Digital Object Identifier: doi:10.1016/j.jmaa.2005.09.090

X. Zhang, L. Chen, and A. U. Neumann, ``The stage-structured predator-prey model and optimal harvesting policy,'' Mathematical Biosciences, vol. 168, no. 2, pp. 201--210, 2000.

Mathematical Reviews (MathSciNet): MR1802141

Zentralblatt MATH: 0961.92037

Digital Object Identifier: doi:10.1016/S0025-5564(00)00033-X

F. Chen, ``Permanence of periodic Holling type predator-prey system with stage structure for prey,'' Applied Mathematics and Computation, vol. 182, no. 2, pp. 1849--1860, 2006.

Mathematical Reviews (MathSciNet): MR2282627

Zentralblatt MATH: 1111.34039

Digital Object Identifier: doi:10.1016/j.amc.2006.06.024

F. Chen and M. You, ``Permanence, extinction and periodic solution of the predator-prey system with Beddington-DeAngelis functional response and stage structure for prey,'' Nonlinear Analysis: Real World Applications, vol. 9, no. 2, pp. 207--221, 2008.

Mathematical Reviews (MathSciNet): MR2382372

Zentralblatt MATH: 1142.34051

Digital Object Identifier: doi:10.1016/j.nonrwa.2006.09.009

W. S. Yang, X. P. Li, and Z. J. Bai, ``Permanence of periodic Holling type-IV čommentComment on ref. [11?]: We updated the information of this reference. Please check. predator-prey system with stage structure for prey,'' Mathematical and Computer Modelling, vol. 48, no. 5-6, pp. 677--684, 2008.

Mathematical Reviews (MathSciNet): MR2451105

Zentralblatt MATH: 1156.34327

Digital Object Identifier: doi:10.1016/j.mcm.2007.11.003

G. J. Lin and Y. G. Hong, ``Periodic solutions in non čommentComment on ref. [9?]: Please update the information of this reference, if possible. autonomous predator prey system with delays,'' Nonlinear Analysis: Real World Applications. In press.

J. Cui, ``The effect of dispersal on permanence in a predator-prey population growth model,'' Computers & Mathematics with Applications, vol. 44, no. 8-9, pp. 1085--1097, 2002.

Mathematical Reviews (MathSciNet): MR1937569

Zentralblatt MATH: 1032.92032

J. Cui, L. Chen, and W. Wang, ``The effect of dispersal on population growth with stage-structure,'' Computers & Mathematics with Applications, vol. 39, no. 1-2, pp. 91--102, 2000.

Mathematical Reviews (MathSciNet): MR1729421

Zentralblatt MATH: 0968.92018

X.-Q. Zhao, ``The qualitative analysis of $n$-species Lotka-Volterra periodic competition systems,'' Mathematical and Computer Modelling, vol. 15, no. 11, pp. 3--8, 1991. \endthebibliography

Mathematical Reviews (MathSciNet): MR1137655

Zentralblatt MATH: 0756.34048

Digital Object Identifier: doi:10.1016/0895-7177(91)90100-L

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