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Optimal Harvesting and Stability for a Predator-prey System with Stage Structure

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Abstract

The dynamics of a predator-prey system, where prey population has two stages, an immature stage and a mature stage with harvesting, the growth of predator population is of Lotka-Volterra nature, are modelled by a system of retarded functional differential equations. We obtain conditions for global asymptotic stability of three nonnegative equilibria and a threshold of harvesting for the mature prey population. The effect of delay on the population at positive equilibrium and the optimal harvesting of the mature prey population are also considered.

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Authors and Affiliations

  1. Department of Mathematics, Xinyang Teachers College, Henan, 464000, China

    Xin-yu Song

  2. Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080, China

    Lan-sun Chen

Authors
  1. Xin-yu Song
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  2. Lan-sun Chen
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Correspondence to Xin-yu Song.

Additional information

Supported by the National Natural Science Foundation of China (No. 10171106) and the Natural Science Foundation of Henan Province (No. 0211010400).

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Song, Xy., Chen, Ls. Optimal Harvesting and Stability for a Predator-prey System with Stage Structure. Acta Mathematicae Applicatae Sinica, English Series 18, 423–430 (2002). https://doi.org/10.1007/s102550200042

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  • DOI: https://doi.org/10.1007/s102550200042

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