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

Author

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  • 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
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    References listed on IDEAS

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    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. 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.
    4. 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.
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