IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i8p1247-d790727.html
   My bibliography  Save this article

Qualitative Analysis of a Model of Renewable Resources and Population with Distributed Delays

Author

Listed:
  • Tiziana Ciano

    (Department of Law, Economics and Human Sciences, University “Mediterranea” of Reggio Calabria, Via dell’Università, 25, 89124 Reggio Calabria, Italy
    Decision Lab, University “Mediterranea” of Reggio Calabria, Via dell’Università, 25, 89124 Reggio Calabria, Italy)

  • Massimiliano Ferrara

    (Department of Law, Economics and Human Sciences, University “Mediterranea” of Reggio Calabria, Via dell’Università, 25, 89124 Reggio Calabria, Italy
    Decision Lab, University “Mediterranea” of Reggio Calabria, Via dell’Università, 25, 89124 Reggio Calabria, Italy
    Department of Management and Technology, ICRIOS-The Invernizzi Centre for Research in Innovation, Organization, Strategy and Entrepreneurship Bocconi University, Via Sarfatti, 25, 20136 Milano, Italy)

  • Luca Guerrini

    (Decision Lab, University “Mediterranea” of Reggio Calabria, Via dell’Università, 25, 89124 Reggio Calabria, Italy
    Department of Management, Polytechnic University of Marche, Piazzale Martelli 8, 60121 Ancona, Italy)

Abstract

This work generalizes Matsumoto et al.’s dynamic model of population and renewable resources by substituting a distributed delay for the time delay. It is proved that the equilibrium point may lose or gain local stability, allowing for the observation of alternating stability/instability areas if some conditions hold.

Suggested Citation

  • Tiziana Ciano & Massimiliano Ferrara & Luca Guerrini, 2022. "Qualitative Analysis of a Model of Renewable Resources and Population with Distributed Delays," Mathematics, MDPI, vol. 10(8), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1247-:d:790727
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/8/1247/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/8/1247/
    Download Restriction: no
    ---><---

    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. Invernizzi, Sergio & Medio, Alfredo, 1991. "On lags and chaos in economic dynamic models," Journal of Mathematical Economics, Elsevier, vol. 20(6), pages 521-550.
    3. R. Morris Coats & Thomas R. Dalton, 2000. "Could institutional reform have saved Easter Island?," Journal of Evolutionary Economics, Springer, vol. 10(5), pages 489-505.
    4. Akio Matsumoto & Mami Suzuki & Yasuhisa Saito, 2007. "Time-Delayed Dynamic Model of Renewable Resource and Population," Springer Books, in: Toichiro Asada & Toshiharu Ishikawa (ed.), Time and Space in Economics, chapter 8, pages 145-159, Springer.
    5. Reuveny, Rafael & Decker, Christopher S., 2000. "Easter Island: historical anecdote or warning for the future?," Ecological Economics, Elsevier, vol. 35(2), pages 271-287, November.
    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. Bruno Antonio Pansera & Massimiliano Ferrara & Luca Guerrini & Tiziana Ciano, 2023. "Preface to the Special Issue on “Differential Games and Its Applications”," Mathematics, MDPI, vol. 11(13), pages 1-4, July.
    2. Linna Liu & Feiqi Deng & Boyang Qu & Yanhong Meng, 2022. "Fundamental Properties of Nonlinear Stochastic Differential Equations," Mathematics, MDPI, vol. 10(15), pages 1-18, July.

    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. David Croix & Davide Dottori, 2008. "Easter Island’s collapse: a tale of a population race," Journal of Economic Growth, Springer, vol. 13(1), pages 27-55, March.
    2. Pezzey, John C. V. & Anderies, John M., 2003. "The effect of subsistence on collapse and institutional adaptation in population-resource societies," Journal of Development Economics, Elsevier, vol. 72(1), pages 299-320, October.
    3. Roman, Sabin & Bullock, Seth & Brede, Markus, 2017. "Coupled Societies are More Robust Against Collapse: A Hypothetical Look at Easter Island," Ecological Economics, Elsevier, vol. 132(C), pages 264-278.
    4. Kuil, Linda & Carr, Gemma & Prskawetz, Alexia & Salinas, José Luis & Viglione, Alberto & Blöschl, Günter, 2019. "Learning from the Ancient Maya: Exploring the Impact of Drought on Population Dynamics," Ecological Economics, Elsevier, vol. 157(C), pages 1-16.
    5. Dalton, Thomas R. & Coats, R. Morris & Asrabadi, Badiollah R., 2005. "Renewable resources, property-rights regimes and endogenous growth," Ecological Economics, Elsevier, vol. 52(1), pages 31-41, January.
    6. Late Lawson & Lawson Late, 2020. "A simple Ricardo-Malthusian model of population, deforestation and biodiversity loss," Working Papers 2020.08, FAERE - French Association of Environmental and Resource Economists.
    7. Zachary Dockstader & Chris T. Bauch & Madhur Anand, 2019. "Interconnections Accelerate Collapse in a Socio-Ecological Metapopulation," Sustainability, MDPI, vol. 11(7), pages 1-13, March.
    8. Nagase, Yoko & Uehara, Takuro, 2011. "Evolution of population-resource dynamics models," Ecological Economics, Elsevier, vol. 72(C), pages 9-17.
    9. D'Alessandro, Simone, 2007. "Non-linear dynamics of population and natural resources: The emergence of different patterns of development," Ecological Economics, Elsevier, vol. 62(3-4), pages 473-481, May.
    10. James A. Brander, 2007. "Viewpoint: Sustainability: Malthus revisited?," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 40(1), pages 1-38, February.
    11. Fletcher, C.S. & Hilbert, David W., 2007. "Resilience in landscape exploitation systems," Ecological Modelling, Elsevier, vol. 201(3), pages 440-452.
    12. Rafael Reuveny & John W. Maxwell, 2001. "Conflict and Renewable Resources," Journal of Conflict Resolution, Peace Science Society (International), vol. 45(6), pages 719-742, December.
    13. López, Ramón & Schiff, Maurice, 2013. "Interactive dynamics between natural and man-made assets: The impact of external shocks," Journal of Development Economics, Elsevier, vol. 104(C), pages 1-15.
    14. Takuro Uehara & Yoko Nagase & Wayne Wakeland, 2016. "Integrating Economics and System Dynamics Approaches for Modelling an Ecological–Economic System," Systems Research and Behavioral Science, Wiley Blackwell, vol. 33(4), pages 515-531, July.
    15. Pietro Peretto & Simone Valente, 2015. "Growth on a finite planet: resources, technology and population in the long run," Journal of Economic Growth, Springer, vol. 20(3), pages 305-331, September.
    16. Zijin Xie, 2022. "Government intervention in wildlife damage management: a bioeconomic analysis of wildlife damage compensation and taxation policies," Journal of Bioeconomics, Springer, vol. 24(1), pages 93-115, April.
    17. Roman, Sabin & Palmer, Erika & Brede, Markus, 2018. "The Dynamics of Human–Environment Interactions in the Collapse of the Classic Maya," Ecological Economics, Elsevier, vol. 146(C), pages 312-324.
    18. Erin L. Wolcott & Jon M. Conrad, 2011. "Agroecology of an Island Economy," Land Economics, University of Wisconsin Press, vol. 87(3), pages 403-411.
    19. Pakandam, Barzin, 2009. "Why Easter Island collapsed: an answer for an enduring question," Economic History Working Papers 27864, London School of Economics and Political Science, Department of Economic History.
    20. Cyrus Chu, C.Y. & Lai, Ching-Chong & Liao, Chih-Hsing, 2014. "How could the non-sustainable Easter Island have been sustained?," International Review of Economics & Finance, Elsevier, vol. 34(C), pages 161-174.

    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:gam:jmathe:v:10:y:2022:i:8:p:1247-:d:790727. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.