IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v512y2018icp1216-1239.html

Modeling and dynamical analysis of a triple delayed prey–predator–scavenger system with Lévy jumps

Author

Listed:
  • Liu, Chao
  • Wang, Luping
  • Zhang, Qingling
  • Li, Yuanke

Abstract

In this paper, a hybrid triple delayed prey–predator–scavenger system with commercial harvesting and Lévy jumps is established, where both maturation delay for prey population and gestation delays for predator and scavenger population are considered. For deterministic system, positivity and uniform permanence of solution are discussed. Local stability analysis of deterministic system around interior equilibrium is investigated due to variations of triple time delays. For stochastic system without time delay, sufficient conditions for stochastically ultimate boundedness and stochastic permanence are discussed. For stochastic system with triple time delays, existence and uniqueness of global positive solution are studied. By constructing appropriate Lyapunov functions, asymptotic behavior of the hybrid stochastic system with triple time delays and Lévy jumps is discussed. Numerical simulations are supported to illustrate theoretical results.

Suggested Citation

  • Liu, Chao & Wang, Luping & Zhang, Qingling & Li, Yuanke, 2018. "Modeling and dynamical analysis of a triple delayed prey–predator–scavenger system with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 1216-1239.
    • Handle: RePEc:eee:phsmap:v:512:y:2018:i:c:p:1216-1239
    DOI: 10.1016/j.physa.2018.08.040
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437118309865
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2018.08.040?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Zhou, Yanli & Yuan, Sanling & Zhao, Dianli, 2016. "Threshold behavior of a stochastic SIS model with Le´vy jumps," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 255-267.
    2. Liu, Chao & Lu, Na & Zhang, Qingling & Li, Jinna & Liu, Peiyong, 2016. "Modeling and analysis in a prey–predator system with commercial harvesting and double time delays," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 77-101.
    3. Liu, Chao & Lu, Na & Zhang, Qingling, 2017. "Dynamical analysis in a hybrid bioeconomic system with multiple time delays and strong Allee effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 136(C), pages 104-131.
    4. H. Scott Gordon, 1954. "The Economic Theory of a Common-Property Resource: The Fishery," Palgrave Macmillan Books, in: Chennat Gopalakrishnan (ed.), Classic Papers in Natural Resource Economics, chapter 9, pages 178-203, Palgrave Macmillan.
    5. H. Scott Gordon, 1954. "The Economic Theory of a Common-Property Resource: The Fishery," Journal of Political Economy, University of Chicago Press, vol. 62(2), pages 124-124.
    6. Liu, Chao & Yu, Longfei & Zhang, Qingling & Li, Yuanke, 2018. "Dynamic analysis of a hybrid bioeconomic plankton system with double time delays and stochastic fluctuations," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 115-137.
    7. Yu, Jingyi & Liu, Meng, 2017. "Stationary distribution and ergodicity of a stochastic food-chain model with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 14-28.
    8. Zhang, Yue & Zhang, Qingling & Yan, Xing-Gang, 2014. "Complex dynamics in a singular Leslie–Gower predator–prey bioeconomic model with time delay and stochastic fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 404(C), pages 180-191.
    9. Zhang, Yue & Zheng, Yan & Liu, Xi & Zhang, Qingling & Li, Aihua, 2016. "Dynamical analysis of a differential algebraic bio-economic model with stage-structured and stochastic fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 222-229.
    10. Zhao, Hongyong & Zhang, Xuebing & Huang, Xuanxuan, 2015. "Hopf bifurcation and spatial patterns of a delayed biological economic system with diffusion," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 462-480.
    11. Qiu, Hong & Deng, Wenmin, 2018. "Optimal harvesting of a stochastic delay competitive Lotka–Volterra model with Lévy jumps," Applied Mathematics and Computation, Elsevier, vol. 317(C), pages 210-222.
    12. Liu, Lidan & Meng, Xinzhu & Zhang, Tonghua, 2017. "Optimal control strategy for an impulsive stochastic competition system with time delays and jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 99-113.
    13. Xinyou Meng & Qingling Zhang, 2015. "Complex Dynamics in a Singular Delayed Bioeconomic Model with and without Stochastic Fluctuation," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-15, October.
    14. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2016. "Asymptotic behavior of a stochastic delayed SEIR epidemic model with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 870-882.
    15. Liu, Meng & Bai, Chuanzhi & Deng, Meiling & Du, Bo, 2016. "Analysis of stochastic two-prey one-predator model with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 176-188.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Liu, Chao & Xun, Xinying & Zhang, Guilai & Li, Yuanke, 2020. "Stochastic dynamics and optimal control in a hybrid bioeconomic system with telephone noise and Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Liu, Chao & Xun, Xinying & Zhang, Qingling & Li, Yuanke, 2019. "Dynamical analysis and optimal control in a hybrid stochastic double delayed bioeconomic system with impulsive contaminants emission and Lévy jumps," Applied Mathematics and Computation, Elsevier, vol. 352(C), pages 99-118.
    2. Liu, Chao & Xun, Xinying & Zhang, Guilai & Li, Yuanke, 2020. "Stochastic dynamics and optimal control in a hybrid bioeconomic system with telephone noise and Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    3. Liu, Chao & Yu, Longfei & Zhang, Qingling & Li, Yuanke, 2018. "Dynamic analysis of a hybrid bioeconomic plankton system with double time delays and stochastic fluctuations," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 115-137.
    4. Liu, Chao & Wang, Luping & Zhang, Qingling & Yan, Yun, 2017. "Dynamical analysis in a bioeconomic phytoplankton zooplankton system with double time delays and environmental stochasticity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 682-698.
    5. Nosrati, Komeil & Shafiee, Masoud, 2017. "Dynamic analysis of fractional-order singular Holling type-II predator–prey system," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 159-179.
    6. John Lynham, 2012. "Ecomarkets For Conservation And Sustainable Development in the Coastal Zone," Working Papers 201218, University of Hawaii at Manoa, Department of Economics.
    7. Kotchen, Matthew J. & Salant, Stephen W., 2011. "A free lunch in the commons," Journal of Environmental Economics and Management, Elsevier, vol. 61(3), pages 245-253, May.
    8. Per Sandberg, 2006. "Variable unit costs in an output-regulated industry: The Fishery," Applied Economics, Taylor & Francis Journals, vol. 38(9), pages 1007-1018.
    9. David Corderí Novoa., 2008. "Deforestation and Property Rights: A Comparison between Former British and Spanish Colonies," Economic Analysis Working Papers (2002-2010). Atlantic Review of Economics (2011-2016), Colexio de Economistas de A Coruña, Spain and Fundación Una Galicia Moderna, vol. 7, pages 1-14, July.
    10. Holland, Daniel S. & Herrera, Guillermo E., 2012. "The impact of age structure, uncertainty, and asymmetric spatial dynamics on regulatory performance in a fishery metapopulation," Ecological Economics, Elsevier, vol. 77(C), pages 207-218.
    11. Schnier, Kurt Erik, 2009. "Spatial externalities and the common-pool resource mechanism," Journal of Economic Behavior & Organization, Elsevier, vol. 70(1-2), pages 402-415, May.
    12. Wang, Ying & Hu, Jianfeng & Pan, Haoran & Li, Shiyu & Failler, Pierre, 2016. "An integrated model for marine fishery management in the Pearl River Estuary: Linking socio-economic systems and ecosystems," Marine Policy, Elsevier, vol. 64(C), pages 135-147.
    13. Buchanan, James M. & Yoon, Yong J., 2004. "Majoritarian exploitation of the fiscal commons: general taxes-differential transfers," European Journal of Political Economy, Elsevier, vol. 20(1), pages 73-90, March.
    14. Mahabile, M. & Lyne, Michael C. & Panin, A., 2005. "An empirical analysis of factors affecting the productivity of livestock in southern Botswana," Agrekon, Agricultural Economics Association of South Africa (AEASA), vol. 44(01), pages 1-19, March.
    15. Castle, Emery N. & Kelso, Maurice M. & Stevens, Joe B. & Stoevener, Herbert H., 1981. "PART III. Natural Resource Economics, 1946-75," AAEA Monographs, Agricultural and Applied Economics Association, number 337228, June.
    16. Hoff Karla, 2010. "Dysfunctional Finance: Positive Shocks and Negative Outcomes," Journal of Globalization and Development, De Gruyter, vol. 1(1), pages 1-24, January.
    17. Amitrajeet A. Batabyal & Henk Folmer, 2019. "Space and the environment: an introduction to the topical collection," Letters in Spatial and Resource Sciences, Springer, vol. 12(1), pages 1-7, April.
    18. McCloskey Deirdre Nansen, 2018. "The Two Movements in Economic Thought, 1700–2000: Empty Economic Boxes Revisited," Man and the Economy, De Gruyter, vol. 5(2), pages 1-20, December.
    19. Carlson, Ernest W., 1971. "The Biological and Economic Objectives of Fishery Management," File Manuscripts, United States National Marine Fisheries Service, Economic Research Division, number 233587, December.
    20. Coxhead, Ian A. & Jayasuriya, Sisira, 2003. "Trade, Liberalization, Resource Degradation and Industrial Pollution in Developing Countries: An Integrated Analysis," Staff Papers 12691, University of Wisconsin-Madison, Department of Agricultural and Applied Economics.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:512:y:2018:i:c:p:1216-1239. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.