IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v266y2015icp462-480.html
   My bibliography  Save this article

Hopf bifurcation and spatial patterns of a delayed biological economic system with diffusion

Author

Listed:
  • Zhao, Hongyong
  • Zhang, Xuebing
  • Huang, Xuanxuan

Abstract

In this paper, a delayed biological economic system which considers a plankton system with harvest effort on phytoplankton is proposed. By using the theory of partial functional differential equations, Hopf bifurcation of the proposed system with delay as the bifurcation parameter is investigated. It reveals that the discrete time delay has a destabilizing effect in the plankton dynamics, and a phenomenon of Hopf bifurcation occurs as the delay increases through a certain threshold. Then by numerical simulations the impact of delay, diffusion and economic interest on plankton system are explored. It is found that delay can cause system into chaos and can trigger the emergence of irregular spatial patterns via a Hopf bifurcation. Moreover, diffusion and economic profit can also affect the dynamic behavior of the system.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:462-480
    DOI: 10.1016/j.amc.2015.05.089
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315007134
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.05.089?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. Upadhyay, Ranjit Kumar & Kumari, Nitu & Rai, Vikas, 2009. "Wave of chaos in a diffusive system: Generating realistic patterns of patchiness in plankton–fish dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 262-276.
    2. Gao, Shujing & Chen, Lansun, 2005. "The effect of seasonal harvesting on a single-species discrete population model with stage structure and birth pulses," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 1013-1023.
    3. 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.
    4. 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.
    5. 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.
    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. Huang, Chengdai & Cao, Jinde & Xiao, Min & Alsaedi, Ahmed & Alsaadi, Fuad E., 2017. "Controlling bifurcation in a delayed fractional predator–prey system with incommensurate orders," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 293-310.
    2. Han, Renji & Dai, Binxiang, 2017. "Spatiotemporal dynamics and spatial pattern in a diffusive intraguild predation model with delay effect," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 177-201.
    3. Huang, Tousheng & Zhang, Huayong, 2016. "Bifurcation, chaos and pattern formation in a space- and time-discrete predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 92-107.
    4. 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.
    5. 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.
    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.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Barkley Rosser, J. Jr., 2001. "Complex ecologic-economic dynamics and environmental policy," Ecological Economics, Elsevier, vol. 37(1), pages 23-37, April.
    6. 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.
    7. 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.
    8. repec:mse:cesdoc:13002r is not listed on IDEAS
    9. 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.
    10. 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.
    11. 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.
    12. Catherine J. Morrison Paul & Ronald G. Felthoven & Marcelo de O. Torres, 2010. "Productive performance in fisheries: modeling, measurement, and management," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 54(3), pages 343-360, July.
    13. Davis, Katrina & Pannell, David J. & Kragt, Marit & Gelcich, Stefan & Schilizzi, Steven, 2014. "Accounting for enforcement is essential to improve the spatial allocation of marine restricted-use zoning systems," Working Papers 195718, University of Western Australia, School of Agricultural and Resource Economics.
    14. Lee, Kun C. & Short, Cameron & Heady, Earl O., 1981. "Optimal Groundwater Mining In The Ogallala Aquifer: Estimation Of Economic Losses And Excessive Depletion Due To Commonality," 1981 Annual Meeting, July 26-29, Clemson, South Carolina 279261, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    15. Eppink, Florian V. & van den Bergh, Jeroen C.J.M., 2007. "Ecological theories and indicators in economic models of biodiversity loss and conservation: A critical review," Ecological Economics, Elsevier, vol. 61(2-3), pages 284-293, March.
    16. Marco Casari, 2002. "Can genetic algorithms explain experimental anomalies? An application to common property resources," UFAE and IAE Working Papers 542.02, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    17. van Dijk, Diana & Hendrix, Eligius M.T. & Haijema, Rene & Groeneveld, Rolf A. & van Ierland, Ekko C., 2014. "On solving a bi-level stochastic dynamic programming model for analyzing fisheries policies: Fishermen behavior and optimal fish quota," Ecological Modelling, Elsevier, vol. 272(C), pages 68-75.
    18. Tarui, Nori & Mason, Charles F. & Polasky, Stephen & Ellis, Greg, 2008. "Cooperation in the commons with unobservable actions," Journal of Environmental Economics and Management, Elsevier, vol. 55(1), pages 37-51, January.
    19. Salzberger Eli M., 2011. "The Law and Economics Analysis of Intellectual Property: Paradigmatic Shift From Incentives to Traditional Property," Review of Law & Economics, De Gruyter, vol. 7(2), pages 435-480, December.
    20. Daniel W. Bromley, 1982. "Land and Water Problems: An Institutional Perspective," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 64(5), pages 834-844.
    21. Pies, Ingo, 2012. "Optimierung versus Koordinierung: Zur ordonomischen Klärung des wirtschaftsethischen Problems," Discussion Papers 2012-21, Martin Luther University of Halle-Wittenberg, Chair of Economic Ethics.

    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:apmaco:v:266:y:2015:i:c:p:462-480. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.