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

Carlos Ramirez-Carrasco (), Fernando Córdova-Lepe and Nelson Velásquez
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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

Mathematics, 2022, vol. 10, issue 19, 1-10

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.

Keywords: mathematical model; local stability; migration; noise; Lombard effect; occupancy level (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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