IDEAS home Printed from https://ideas.repec.org/a/wly/jnljam/v2014y2014i1n852025.html

Local Hopf Bifurcation in a Competitive Model of Market Structure with Consumptive Delays

Author

Listed:
  • Xuhui Li

Abstract

A competitive model of market structure with consumptive delays is considered. The local stability of the positive equilibrium and the existence of local Hopf bifurcation are investigated by analyzing the distribution of the roots of the associated characteristic equation. The explicit formulas determining the stability and other properties of bifurcating periodic solutions are derived by using normal form theory and center manifold argument. Finally, numerical simulations are given to support the analytical results.

Suggested Citation

  • Xuhui Li, 2014. "Local Hopf Bifurcation in a Competitive Model of Market Structure with Consumptive Delays," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:852025
    DOI: 10.1155/2014/852025
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2014/852025
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/852025?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
    ---><---

    References listed on IDEAS

    as
    1. Brander, James A & Taylor, M Scott, 1998. "The Simple Economics of Easter Island: A Ricardo-Malthus Model of Renewable Resource Use," American Economic Review, American Economic Association, vol. 88(1), pages 119-138, March.
    2. Doriana Delfino & Peter J. Simmons, "undated". "Infectious disease and economic growth: the case of tuberculosis," Discussion Papers 99/23, Department of Economics, University of York.
    3. J. Doyne Farmer, 2000. "A Simple Model For The Nonequilibrium Dynamics And Evolution Of A Financial Market," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 425-441.
    Full references (including those not matched with items on IDEAS)

    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. Brian C. O'Neill & Deborah Balk & Melanie Brickman & Markos Ezra, 2001. "A Guide to Global Population Projections," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 4(8), pages 203-288.
    2. repec:tiu:tiutis:fe79a9d2-e9e3-4dbc-9539-cdece886993d is not listed on IDEAS
    3. Nils‐Petter Lagerlöf & Thomas Tangerås, 2008. "From rent seeking to human capital: a model where resource shocks cause transitions from stagnation to growth," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 41(3), pages 760-780, August.
    4. Partha Dasgupta & Tapan Mitra & Gerhard Sorger, 2019. "Harvesting the Commons," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 72(3), pages 613-636, March.
    5. Pedro, de Mendonça, 2009. "Self-Enforcing Climate Change Treaties: A Generalized Differential Game Approach with Applications," MPRA Paper 17889, University Library of Munich, Germany.
    6. Nils-Petter Lagerlof, 2002. "The Roads To and From Serfdom," Macroeconomics 0212011, University Library of Munich, Germany.
    7. Xu, Si & He, Xiaoyi & Xiong, Feng & Chen, Peiyao, 2024. "CEOs’ early-life famine experience and corporate donations: Evidence from the great Chinese famine," Economic Modelling, Elsevier, vol. 130(C).
    8. Xiaojie Chen & Attila Szolnoki, 2018. "Punishment and inspection for governing the commons in a feedback-evolving game," PLOS Computational Biology, Public Library of Science, vol. 14(7), pages 1-15, July.
    9. Schiff, Maurice, 2021. "Low, High and Super Congestion of a Renewable Natural Resource under Autarky and Trade," IZA Discussion Papers 14279, IZA Network @ LISER.
    10. Knapp, Keith C., 2006. "Recursive Sustainability: Intertemporal Efficiency and Equity," 2006 Annual meeting, July 23-26, Long Beach, CA 21472, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    11. Fletcher, C.S. & Hilbert, David W., 2007. "Resilience in landscape exploitation systems," Ecological Modelling, Elsevier, vol. 201(3), pages 440-452.
    12. Wei-Bin Zhang, 2015. "Oscillations in a Growth Model with Endogenous Wealth, Resource, Housing, and Elastic Labour Supply," International Journal of Economics and Empirical Research (IJEER), The Economics and Social Development Organization (TESDO), vol. 3(9), pages 458-472, September.
    13. Richard D. Horan & Jason F. Shogren & Erwin Bulte, 2003. "A Paleoeconomic Theory of Co‐Evolution and Extinction of Domesticable Animals," Scottish Journal of Political Economy, Scottish Economic Society, vol. 50(2), pages 131-148, May.
    14. Lafuite, A.-S. & Loreau, M., 2017. "Time-delayed biodiversity feedbacks and the sustainability of social-ecological systems," Ecological Modelling, Elsevier, vol. 351(C), pages 96-108.
    15. Juan Miguel Benito-Ostolaza & Nuria Osés-Eraso, 2013. "Incentives to give up resource extraction and avoid the tragedy of the commons," Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra 1305, Departamento de Economía - Universidad Pública de Navarra.
    16. Ratbek Dzhumashev & Gennadi Kazakevitch, 2025. "Production, Environment, and Population Growth," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 88(11), pages 2791-2814, November.
    17. Petros G. Sekeris, 2014. "The tragedy of the commons in a violent world," RAND Journal of Economics, RAND Corporation, vol. 45(3), pages 521-532, September.
    18. Schiff, Maurice, 2025. "Migration and Population Growth's Impact on Natural Resources and Welfare: The Role of Manufacturing's Returns to Scale," GLO Discussion Paper Series 1701, Global Labor Organization (GLO).
    19. Hartwick, John M. & Van Long, Ngo & Tian, Huilan, 2001. "Deforestation and Development in a Small Open Economy," Journal of Environmental Economics and Management, Elsevier, vol. 41(3), pages 235-251, May.
    20. Lasserre, Pierre & Soubeyran, Antoine, 2003. "A Ricardian model of the tragedy of the commons," Journal of Economic Behavior & Organization, Elsevier, vol. 50(1), pages 29-45, January.
    21. Yasuhiro Nakamoto & Koichi Futagami, 2016. "Dynamic Analysis of a Renewable Resource in a Small Open Economy: The Role of Environmental Policies for the Environment," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 64(3), pages 373-399, July.

    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:wly:jnljam:v:2014:y:2014:i:1:n:852025. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4185 .

    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.