IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v40y2009i3p1309-1318.html
   My bibliography  Save this article

Bifurcations of a class of singular biological economic models

Author

Listed:
  • Zhang, Xue
  • Zhang, Qing-ling
  • Zhang, Yue

Abstract

This paper studies systematically a prey–predator singular biological economic model with time delay. It shows that this model exhibits two bifurcation phenomena when the economic profit is zero. One is transcritical bifurcation which changes the stability of the system, and the other is singular induced bifurcation which indicates that zero economic profit brings impulse, i.e., rapid expansion of the population in biological explanation. On the other hand, if the economic profit is positive, at a critical value of bifurcation parameter, the system undergoes a Hopf bifurcation, i.e., the increase of delay destabilizes the system and bifurcates into small amplitude periodic solution. Finally, by using Matlab software, numerical simulations illustrate the effectiveness of the results obtained here. In addition, we study numerically that the system undergoes a saddle-node bifurcation when the bifurcation parameter goes through critical value of positive economic profit.

Suggested Citation

  • Zhang, Xue & Zhang, Qing-ling & Zhang, Yue, 2009. "Bifurcations of a class of singular biological economic models," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1309-1318.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:3:p:1309-1318
    DOI: 10.1016/j.chaos.2007.09.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077907007333
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2007.09.010?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Zhang, Chunrui & Zu, Yuangang & Zheng, Baodong, 2006. "Stability and bifurcation of a discrete red blood cell survival model," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 386-394.
    2. Huang, Chuangxia & Huang, Lihong & Feng, Jianfeng & Nai, Mingyong & He, Yigang, 2007. "Hopf bifurcation analysis for a two-neuron network with four delays," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 795-812.
    3. Jing, Zhujun & Yang, Jianping, 2006. "Bifurcation and chaos in discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 259-277.
    4. Zhang, Yue & Zhang, Qingling & Zhao, Lichun & Yang, Chunyu, 2007. "Dynamical behaviors and chaos control in a discrete functional response model," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1318-1327.
    5. 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.
    6. Sun, Chengjun & Lin, Yiping & Han, Maoan, 2006. "Stability and Hopf bifurcation for an epidemic disease model with delay," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 204-216.
    7. 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.
    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. Grigorii A. Vasilev & Aleksandra A. Filkova & Anastasia N. Sveshnikova, 2021. "Study of Reversible Platelet Aggregation Model by Nonlinear Dynamics," Mathematics, MDPI, vol. 9(7), pages 1-12, April.
    2. Zhang, Xue & Zhang, Qing-Ling & Liu, Chao & Xiang, Zhong-Yi, 2009. "Bifurcations of a singular prey–predator economic model with time delay and stage structure," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1485-1494.
    3. 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.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Busch, Jonah, 2008. "Gains from configuration: The transboundary protected area as a conservation tool," Ecological Economics, Elsevier, vol. 67(3), pages 394-404, October.
    7. Rauscher, Michael, 1996. "Sustainable Development and Complex Ecosystems. An Economist's View," Thuenen-Series of Applied Economic Theory 02, University of Rostock, Institute of Economics.
    8. Squires, Dale & Vestergaard, Niels, 2013. "Technical change in fisheries," Marine Policy, Elsevier, vol. 42(C), pages 286-292.
    9. De Alessi, Michael & Sullivan, Joseph M. & Hilborn, Ray, 2014. "The legal, regulatory, and institutional evolution of fishing cooperatives in Alaska and the West Coast of the United States," Marine Policy, Elsevier, vol. 43(C), pages 217-225.
    10. B. Rudders, David & Ward, John M., 2015. "Own-price elasticity of open access supply as a long-run measure of fish stock abundance," Marine Policy, Elsevier, vol. 53(C), pages 215-226.
    11. Barkley Rosser, J. Jr., 2001. "Complex ecologic-economic dynamics and environmental policy," Ecological Economics, Elsevier, vol. 37(1), pages 23-37, April.
    12. 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.
    13. Bell, Frederick W. & Nash, Darrel A. & Carlson, Ernest W. & Waugh, Frederick V. & Kinoshita, Richard K. & Fullenbaum, Richard F., 1970. "The Future of the World's Fishery Resources: Forecasts of Demand, Supply and Prices to the Year 2000 with a Discussion of Implications for Public Policy," File Manuscripts, United States National Marine Fisheries Service, Economic Research Division, number 233219.
    14. Jorge Higinio Maldonado & Rocío del Pilar Moreno-Sanchez, 2016. "Exacerbating the Tragedy of the Commons: Private Inefficient Outcomes and Peer Effect in Experimental Games with Fishing Communities," PLOS ONE, Public Library of Science, vol. 11(2), pages 1-17, February.
    15. Strydom, M.B. & Nieuwoudt, W. Lieb, 1998. "An Economic Analysis Of Restructuring The South African Hake Quota Market," Agrekon, Agricultural Economics Association of South Africa (AEASA), vol. 37(3), pages 1-15, September.
    16. Stahn, Hubert & Tomini, Agnes, 2021. "Externality and common-pool resources: The case of artesian aquifers," Journal of Environmental Economics and Management, Elsevier, vol. 109(C).
    17. repec:mse:cesdoc:13002r is not listed on IDEAS
    18. Horan, R.D. & Bulte, E.H., 2004. "Optimal and open access harvesting and multi-use species in a second best world," Other publications TiSEM 95000e50-7225-4f4d-aeaf-a, Tilburg University, School of Economics and Management.
    19. Funk, Matt, 2008. "On the Problem of Sustainable Economic Development: A Theoretical Solution to this Prisoner's Dilemma," MPRA Paper 19025, University Library of Munich, Germany, revised 08 Jun 2008.
    20. Kanchanaroek, Yingluk & Termansen, Mette & Quinn, Claire, 2013. "Property rights regimes in complex fishery management systems: A choice experiment application," Ecological Economics, Elsevier, vol. 93(C), pages 363-373.
    21. Crow White & Christopher Costello, 2014. "Close the High Seas to Fishing?," PLOS Biology, Public Library of Science, vol. 12(3), pages 1-5, March.

    More about this item

    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:chsofr:v:40:y:2009:i:3:p:1309-1318. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.