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

Fangfang Zhu | Zendy; Xinzhu Meng | Zendy; Tonghua Zhang | Zendy

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

Author(s) -

Fangfang Zhu,

Xinzhu Meng,

Tonghua Zhang

Publication year - 2019

Publication title -

mathematical biosciences and engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.451

H-Index - 45

eISSN - 1551-0018

pISSN - 1547-1063

DOI - 10.3934/mbe.2019074

Subject(s) - hessian matrix , stability (learning theory) , mathematics , stochastic modelling , mathematical optimization , computer science , statistics , machine learning

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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