The Optimal Harvesting of a Stochastic Gilpin-Ayala Model Under Regime Switching

Juan Hou; Yanqun Wang; Zhenguo Luo

doi:doi:10.11648/j.sjams.20160406.15

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The Optimal Harvesting of a Stochastic Gilpin-Ayala Model Under Regime Switching

Juan Hou, Yanqun Wang, Zhenguo Luo

Published in Science Journal of Applied Mathematics and Statistics (Volume 4, Issue 6)

Received: 30 September 2016 Accepted: 13 October 2016 Published: 7 November 2016

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Abstract

In this paper, we consider a stochastic Gilpin-Ayala model under regime switching. Obtain the optimal harvesting effort and the maximum sustained yield by investigating the condition of average boundness of the system, and the ergodicity of the Markov chain. Also, through an example, we have proved our conclusion.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 4, Issue 6)
DOI	10.11648/j.sjams.20160406.15
Page(s)	276-283
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Optimal Harvesting, Stochastic Differential Equation, Markov Chain

References

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[4]	T.C, Gard, Stability for multispecies population models in random environments, Nonlinear Anal. 10(1986)1411-1419.
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[6]	D. Jiang, N. Shi, X. Li, Global stability and stochastic permanence of a non-autonomous logistic equation with random perturbation, J. Math. Ana. Appl.,340 (2008) 588-597.
[7]	Y. Takeuchi, N. H, Du, N. T. Hieu, K.Sato,Evolution of predator-prey described by a Lotka-Voterra equation under random environment, J. Math. Ana. Appl., 323 (2006) 938-957.
[8]	Q, Luo. X. Mao, Stochastic population dynamics under regime switching,J. Math. Ana. Appl., 334 (2007) 69-84.
[9]	X. Y. Li, Alison Gray, D. Q. Jiang, X. Mao, Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching, J. Math. Ana. Appl., 376 (2011) 11-28.
[10]	JianhaiBaoa, XMaob, Geroge Yin c, ChengguiYuana, Competitive Lotka–Volterra population dynamics with jumps, Nonlinear Analysis 74 (2011) 6601–6616.

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APA Style

Juan Hou, Yanqun Wang, Zhenguo Luo. (2016). The Optimal Harvesting of a Stochastic Gilpin-Ayala Model Under Regime Switching. Science Journal of Applied Mathematics and Statistics, 4(6), 276-283. https://doi.org/10.11648/j.sjams.20160406.15

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ACS Style

Juan Hou; Yanqun Wang; Zhenguo Luo. The Optimal Harvesting of a Stochastic Gilpin-Ayala Model Under Regime Switching. Sci. J. Appl. Math. Stat. 2016, 4(6), 276-283. doi: 10.11648/j.sjams.20160406.15

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AMA Style

Juan Hou, Yanqun Wang, Zhenguo Luo. The Optimal Harvesting of a Stochastic Gilpin-Ayala Model Under Regime Switching. Sci J Appl Math Stat. 2016;4(6):276-283. doi: 10.11648/j.sjams.20160406.15

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@article{10.11648/j.sjams.20160406.15,
  author = {Juan Hou and Yanqun Wang and Zhenguo Luo},
  title = {The Optimal Harvesting of a Stochastic Gilpin-Ayala Model Under Regime Switching},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {4},
  number = {6},
  pages = {276-283},
  doi = {10.11648/j.sjams.20160406.15},
  url = {https://doi.org/10.11648/j.sjams.20160406.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20160406.15},
  abstract = {In this paper, we consider a stochastic Gilpin-Ayala model under regime switching. Obtain the optimal harvesting effort and the maximum sustained yield by investigating the condition of average boundness of the system, and the ergodicity of the Markov chain. Also, through an example, we have proved our conclusion.},
 year = {2016}
}

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TY  - JOUR
T1  - The Optimal Harvesting of a Stochastic Gilpin-Ayala Model Under Regime Switching
AU  - Juan Hou
AU  - Yanqun Wang
AU  - Zhenguo Luo
Y1  - 2016/11/07
PY  - 2016
N1  - https://doi.org/10.11648/j.sjams.20160406.15
DO  - 10.11648/j.sjams.20160406.15
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 276
EP  - 283
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20160406.15
AB  - In this paper, we consider a stochastic Gilpin-Ayala model under regime switching. Obtain the optimal harvesting effort and the maximum sustained yield by investigating the condition of average boundness of the system, and the ergodicity of the Markov chain. Also, through an example, we have proved our conclusion.
VL  - 4
IS  - 6
ER  -

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Author Information

Juan Hou

College of Mathematics and Statistics, Hengyang Normal University, Hengyang, P. R. China
Yanqun Wang

College of Mathematics and Statistics, Hengyang Normal University, Hengyang, P. R. China
Zhenguo Luo

College of Mathematics and Statistics, Hengyang Normal University, Hengyang, P. R. China

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APA Style

Juan Hou, Yanqun Wang, Zhenguo Luo. (2016). The Optimal Harvesting of a Stochastic Gilpin-Ayala Model Under Regime Switching. Science Journal of Applied Mathematics and Statistics, 4(6), 276-283. https://doi.org/10.11648/j.sjams.20160406.15

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ACS Style

Juan Hou; Yanqun Wang; Zhenguo Luo. The Optimal Harvesting of a Stochastic Gilpin-Ayala Model Under Regime Switching. Sci. J. Appl. Math. Stat. 2016, 4(6), 276-283. doi: 10.11648/j.sjams.20160406.15

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AMA Style

Juan Hou, Yanqun Wang, Zhenguo Luo. The Optimal Harvesting of a Stochastic Gilpin-Ayala Model Under Regime Switching. Sci J Appl Math Stat. 2016;4(6):276-283. doi: 10.11648/j.sjams.20160406.15

Copy | Download

@article{10.11648/j.sjams.20160406.15,
  author = {Juan Hou and Yanqun Wang and Zhenguo Luo},
  title = {The Optimal Harvesting of a Stochastic Gilpin-Ayala Model Under Regime Switching},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {4},
  number = {6},
  pages = {276-283},
  doi = {10.11648/j.sjams.20160406.15},
  url = {https://doi.org/10.11648/j.sjams.20160406.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20160406.15},
  abstract = {In this paper, we consider a stochastic Gilpin-Ayala model under regime switching. Obtain the optimal harvesting effort and the maximum sustained yield by investigating the condition of average boundness of the system, and the ergodicity of the Markov chain. Also, through an example, we have proved our conclusion.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - The Optimal Harvesting of a Stochastic Gilpin-Ayala Model Under Regime Switching
AU  - Juan Hou
AU  - Yanqun Wang
AU  - Zhenguo Luo
Y1  - 2016/11/07
PY  - 2016
N1  - https://doi.org/10.11648/j.sjams.20160406.15
DO  - 10.11648/j.sjams.20160406.15
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 276
EP  - 283
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20160406.15
AB  - In this paper, we consider a stochastic Gilpin-Ayala model under regime switching. Obtain the optimal harvesting effort and the maximum sustained yield by investigating the condition of average boundness of the system, and the ergodicity of the Markov chain. Also, through an example, we have proved our conclusion.
VL  - 4
IS  - 6
ER  -

Copy | Download