IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i19p3485-d923661.html
   My bibliography  Save this article

A Simple Stability Analysis for a Mathematical Model of Migration Due to Noise and Resources

Author

Listed:
  • Carlos Ramirez-Carrasco

    (Departamento de Matemática, Física y Estadística, Facultad de Ciencias Básicas, Universidad Católica del Maule, Talca 3460000, Chile)

  • Fernando Córdova-Lepe

    (Departamento de Matemática, Física y Estadística, Facultad de Ciencias Básicas, Universidad Católica del Maule, Talca 3460000, Chile)

  • Nelson Velásquez

    (Departamento de Biología y Química, Facultad de Ciencias Básicas, Universidad Católica del Maule, Talca 3460000, Chile)

Abstract

This research studies a metapopulation model where each patch is considered a form of fragmentation of the environment produced by the spatio-temporal variability of anthropogenic noise. A deterministic mathematical model is proposed that describes two processes of migration between patches. The first process consists of migration due to chronic critical noise produced by an anthropogenic and biological source (self-generated acoustic signals of higher intensity, due to the Lombard effect). The second process consists of migration due to a higher level of stain occupancy. A simple and classical analysis of the local stability of the model is performed. The results indicate that no subpopulation goes extinct; in fact, a necessary condition for long-term stabilization of the size of the subpopulations is that the noise attenuation rate is higher. Moreover, as long as the noise is of low intensity the differences in the carrying capacity of each patch do not produce substantial, long-term differences in the sizes of the subpopulations. However, as the noise intensity increases, the difference in carrying capacities produce noticeable, long-term differences between subpopulation sizes. Finally, the results are corroborated by numerical simulations.

Suggested Citation

  • Carlos Ramirez-Carrasco & Fernando Córdova-Lepe & Nelson Velásquez, 2022. "A Simple Stability Analysis for a Mathematical Model of Migration Due to Noise and Resources," Mathematics, MDPI, vol. 10(19), pages 1-10, September.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3485-:d:923661
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/19/3485/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/10/19/3485/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jade Read & Gareth Jones & Andrew N. Radford, 2014. "Fitness costs as well as benefits are important when considering responses to anthropogenic noise," Behavioral Ecology, International Society for Behavioral Ecology, vol. 25(1), pages 4-7.
    2. Daniel E. Holt & Carol E. Johnston, 2014. "Evidence of the Lombard effect in fishes," Behavioral Ecology, International Society for Behavioral Ecology, vol. 25(4), pages 819-826.
    3. Das, Amartya & Samanta, G.P., 2018. "Stochastic prey–predator model with additional food for predator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 121-141.
    4. Sanchirico, James N. & Wilen, James E., 2001. "A Bioeconomic Model of Marine Reserve Creation," Journal of Environmental Economics and Management, Elsevier, vol. 42(3), pages 257-276, November.
    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. Ramirez-Carrasco, C. & Córdova-Lepe, F. & Moreno-Gómez, F.N. & Velásquez, N.A., 2022. "A mathematical model for the impact of noise on population dynamics of a single species experiencing Lombard effect," Ecological Modelling, Elsevier, vol. 470(C).
    2. Pelletier, Dominique & Mahevas, Stéphanie & Drouineau, Hilaire & Vermard, Youen & Thebaud, Olivier & Guyader, Olivier & Poussin, Benjamin, 2009. "Evaluation of the bioeconomic sustainability of multi-species multi-fleet fisheries under a wide range of policy options using ISIS-Fish," Ecological Modelling, Elsevier, vol. 220(7), pages 1013-1033.
    3. Das, Amartya & Samanta, G.P., 2021. "Influence of environmental noises on a prey–predator species with predator-dependent carrying capacity in alpine meadow ecosystem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 1294-1316.
    4. Sterner, Thomas, 2007. "Unobserved diversity, depletion and irreversibility The importance of subpopulations for management of cod stocks," Ecological Economics, Elsevier, vol. 61(2-3), pages 566-574, March.
    5. Christopher Costello & Daniel T. Kaffine, 2010. "Marine protected areas in spatial property-rights fisheries ," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 54(3), pages 321-341, July.
    6. Costello, Christopher & Molina, Renato, 2021. "Transboundary marine protected areas," Resource and Energy Economics, Elsevier, vol. 65(C).
    7. W. A. Brock & A. Xepapadeas, 2015. "Modeling Coupled Climate, Ecosystems, and Economic Systems," Working Papers 2015.66, Fondazione Eni Enrico Mattei.
    8. Smith, Martin D. & Zhang, Junjie & Coleman, Felicia C., 2005. "Bayesian Bioeconomics of Marine Reserves," 2005 Annual meeting, July 24-27, Providence, RI 19409, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    9. Liu, Qun & Jiang, Daqing, 2023. "Analysis of a stochastic inshore–offshore hairtail fishery model with Ornstein–Uhlenbeck process," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    10. Roy, Jyotirmoy & Alam, Shariful, 2020. "Fear factor in a prey–predator system in deterministic and stochastic environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    11. Mota, Rui Pedro & Nichols, Rachel, 2023. "Habitat considerations in optimal fisheries recovery," Ecological Economics, Elsevier, vol. 214(C).
    12. Anastasios Xepapadeas & William Brock, 2004. "Spatial Analysis: Development of Descriptive and Normative Methods with Applications to Economic-Ecological Modelling," Working Papers 2004.159, Fondazione Eni Enrico Mattei.
    13. Johannesen, Anne Borge, 2007. "Protected areas, wildlife conservation, and local welfare," Ecological Economics, Elsevier, vol. 62(1), pages 126-135, April.
    14. Nichols, Rachel & Yamazaki, Satoshi & Jennings, Sarah, 2018. "The Role of Precaution in Stock Recovery Plans in a Fishery with Habitat Effect," Ecological Economics, Elsevier, vol. 146(C), pages 359-369.
    15. R. Quentin Grafton & Tom Kompas & Pham Van Ha, 2009. "Cod Today and None Tomorrow: The Economic Value of a Marine Reserve," Land Economics, University of Wisconsin Press, vol. 85(3), pages 454-469.
    16. Reimer, Matthew N. & Haynie, Alan C., 2018. "Mechanisms matter for evaluating the economic impacts of marine reserves," Journal of Environmental Economics and Management, Elsevier, vol. 88(C), pages 427-446.
    17. Anders Skonhoft & Jon Olaf Olaussen, 2005. "Managing a Migratory Species That Is Both a Value and a Pest," Land Economics, University of Wisconsin Press, vol. 81(1).
    18. Anders Skonhoft & Wenting Chen, 2011. "On the management of interconnected wildlife populations," Working Paper Series 12311, Department of Economics, Norwegian University of Science and Technology.
    19. Melstrom, Richard T. & Horan, Richard D., 2012. "Managing Excessive Predation in a Predator-Prey Setting: The Case of Piping Plovers," 2012 Annual Meeting, August 12-14, 2012, Seattle, Washington 123350, Agricultural and Applied Economics Association.
    20. Abbott, Joshua K., 2004. "Spatial Competition In Overlapping Seasonal Fisheries: A Bioeconomic Model Of Fishermen And Regulators," 2004 Annual meeting, August 1-4, Denver, CO 20383, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).

    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:19:p:3485-:d:923661. 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.