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Journal of Mathematical Biology

, Volume 73, Issue 3, pp 597–625 | Cite as

Analysis of a stochastic tri-trophic food-chain model with harvesting

  • Meng Liu
  • Chuanzhi Bai
Article

Abstract

We consider a tri-trophic stochastic food-chain model with harvesting. We first establish critical values between persistence in mean and extinction for each species. The results show that persistence and extinction of a species only depends on the demographic impacts of environmental stochasticity on the species and species at lower tropic levels; however, the mean abundance of a species depends on the impacts of environmental stochasticity at all trophic levels. Then we consider stability in distribution of the model. Finally, we provide a necessary and sufficient condition for existence of optimal harvesting strategy and give the optimal harvesting effort and maximum of sustainable yield. The results show that the optimal harvesting strategy is closely related to the stochastic noises in the model.

Keywords

Stochastic control Optimization under uncertainties  Management of natural resources 

Mathematics Subject Classification

60H10 60H30 92D25 

Notes

Acknowledgments

We are very grateful to Professor Sebastian Schreiber and anonymous referees for their careful reading and valuable comments, which led to an improvement of our paper. We also thank Dr. H.Qiu and Q.Wu for helping us to improve the English exposition.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of Mathematical ScienceHuaiyin Normal UniversityHuaianPeople’s Republic of China
  2. 2.School of Mathematics and StatisticsNortheast Normal UniversityChangchunPeople’s Republic of China

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