Optimal harvesting of a competitive n-species stochastic model with delayed diffusions

Fangfang Zhu; Xinzhu Meng; Tonghua Zhang; Fangfang Zhu; Xinzhu Meng; Tonghua Zhang

doi:10.3934/mbe.2019074

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 3: 1554-1574. doi: 10.3934/mbe.2019074

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Optimal harvesting of a competitive n-species stochastic model with delayed diffusions

1.
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, PR China
2.
Department of Mathematics, Swinburne University of Technology, Hawthorn, VIC 3122 Australia

Received: 03 November 2018 Accepted: 28 January 2019 Published: 25 February 2019

In this study, we propose an n-species stochastic model which considers the influences of the competitions and delayed diffusions among populations on dynamics of species. We then investigate the stochastic dynamics of the model, such as the persistence in mean of the species, and the asymptotic stability in distribution of the model. Then, by using the Hessian matrix and theory of optimal harvesting, we investigate the optimal harvesting problem, obtaining the optimal harvesting effort and the maximum of expectation of sustainable yield (ESY). Finally, we numerically discuss some examples to illustrate our theoretical findings, and conclude our study by a brief discussion.
- stochastic delay model,
- optimal harvesting,
- stability in distribution,
- persistence in the mean
Citation: Fangfang Zhu, Xinzhu Meng, Tonghua Zhang. Optimal harvesting of a competitive n-species stochastic model with delayed diffusions[J]. Mathematical Biosciences and Engineering, 2019, 16(3): 1554-1574. doi: 10.3934/mbe.2019074

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Abstract

In this study, we propose an n-species stochastic model which considers the influences of the competitions and delayed diffusions among populations on dynamics of species. We then investigate the stochastic dynamics of the model, such as the persistence in mean of the species, and the asymptotic stability in distribution of the model. Then, by using the Hessian matrix and theory of optimal harvesting, we investigate the optimal harvesting problem, obtaining the optimal harvesting effort and the maximum of expectation of sustainable yield (ESY). Finally, we numerically discuss some examples to illustrate our theoretical findings, and conclude our study by a brief discussion.

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