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

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
[1] X. Mao, G. Marion, E. Rensgaw, Environmental Brownian noise suppresses explosions in population dynamics, Stochastic Process. AppL. 97(2002)95-110.
[2] X. Mao, Delay population dynamics and environment noise, Stoch, Dyn., 5 (2)(2005)149-162.
[3] X. Mao, G. Marion, E. Rensgaw, Asymptotic behavior of the stochastic Lotka-Volterra model, J. Math. Ana. Appl., 287 (2003) 141-156.
[4] T.C, Gard, Stability for multispecies population models in random environments, Nonlinear Anal. 10(1986)1411-1419.
[5] D. Jiang, N. Shi, A note on nonautonomous logistic equation with random perturbation,. Math. Ana. Appl., 303 (2005) 149-162.
[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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    AU  - Juan Hou
    AU  - Yanqun Wang
    AU  - Zhenguo Luo
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    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.
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Author Information
  • College of Mathematics and Statistics, Hengyang Normal University, Hengyang, P. R. China

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

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

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