Harvesting Control for a Stage-Structured Predator-Prey Model with Ivlev's Functional Response and Impulsive Stocking on Prey

Liu, Kaiyuan; Chen, Lansun

doi:https://doi.org/10.1155/2007/86482

Discrete Dynamics in Nature and Society

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Research Article | Open Access

Volume 2007 | Article ID 086482 | https://doi.org/10.1155/2007/86482

Harvesting Control for a Stage-Structured Predator-Prey Model with Ivlev's Functional Response and Impulsive Stocking on Prey

Kaiyuan Liu^1,2and Lansun Chen¹

Received08 Jul 2007

Accepted17 Oct 2007

Published30 Jan 2008

Abstract

We investigate a delayed stage-structured Ivlev's functional response predator-prey model with impulsive stocking on prey and continuous harvesting on predator. Sufficient conditions of the global attractivity of predator-extinction periodic solution and the permanence of the system are obtained. These results show that the behavior of impulsive stocking on prey plays an important role for the permanence of the system. We also prove that all solutions of the system are uniformly ultimately bounded. Our results provide reliable tactical basis for the biological resource management and enrich the theory of impulsive delay differential equations.

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Copyright

Copyright © 2007 Kaiyuan Liu and Lansun Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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