Abstract and Applied Analysis

Stabilization for a Periodic Predator-Prey System

Sebastian Aniţa and Carmen Oana Tarniceriu

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Abstract

A reaction-diffusion system modelling a predator-prey system in a periodic environment is considered. We are concerned in stabilization to zero of one of the components of the solution, via an internal control acting on a small subdomain, and in the preservation of the nonnegativity of both components.

Article information

Source
Abstr. Appl. Anal., Volume 2007 (2007), Article ID 86183, 17 pages.

Dates
First available in Project Euclid: 27 February 2008

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1204126607

Digital Object Identifier
doi:10.1155/2007/86183

Mathematical Reviews number (MathSciNet)
MR2375448

Zentralblatt MATH identifier
1163.35318

Citation

Aniţa, Sebastian; Tarniceriu, Carmen Oana. Stabilization for a Periodic Predator-Prey System. Abstr. Appl. Anal. 2007 (2007), Article ID 86183, 17 pages. doi:10.1155/2007/86183. https://projecteuclid.org/euclid.aaa/1204126607


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References

  • W. Chen and M. Wang, ``Qualitative analysis of predator-prey models with Beddington-De Angelis functional response and diffusion,'' Mathematical and Computer Modelling, vol. 42, no. 1-2, pp. 31--44, 2005.
  • J.-D. Murray, Mathematical Biology I: An Introduction, vol. 17 of Interdisciplinary Applied Mathematics, Springer, New York, NY, USA, 3rd edition, 2002.
  • H. R. Thieme, Mathematics in Population Biology, Princeton Series in Theoretical and Computational Biology, Princeton University Press, Princeton, NJ, USA, 2003.
  • J. M. Cushing, ``Periodic time-dependent predator-prey systems,'' SIAM Journal on Applied Mathematics, vol. 32, no. 1, pp. 82--95, 1977.
  • M. H. Protter and H. F. Weinberger, Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, USA, 1967.
  • B. Ainseba, F. Heiser, and M. Langlais, ``A mathematical analysis of a predator-prey system in a highly heterogeneous environment,'' Differential and Integral Equations, vol. 15, no. 4, pp. 385--404, 2002.
  • B. Ainseba and S. Aniţa, ``Internal stabilizability for a reaction-diffusion problem modeling a predator-prey system,'' Nonlinear Analysis: Theory, Methods & Applications, vol. 61, no. 4, pp. 491--501, 2005.
  • S. Aniţa and M. Langlais, ``Stabilization strategies for some reaction-diffusion systems,'' submitted to, Nonlinear Analysis: Real World Applications, doi:10.1016/j.nonrwa.2007.09.003.
  • F. Courchamp and G. Sugihara, ``Modelling the biological control of an alien predator to protect island species from extinction,'' Ecological Application, vol. 9, no. 1, pp. 112--123, 1999.
  • V. Barbu, Partial Differential Equations and Boundary Value Problems, vol. 441 of Mathematics and Its Applications, Kluwer, Dordrecht, The Netherlands, 1998.