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

Author

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  • 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
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    References listed on IDEAS

    as
    1. Invernizzi, Sergio & Medio, Alfredo, 1991. "On lags and chaos in economic dynamic models," Journal of Mathematical Economics, Elsevier, vol. 20(6), pages 521-550.
    2. 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.
    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.
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    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.

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