A simple stability analysis for a mathematical model of migration due to noise and resources

Autor
Ramirez-Carrasco, Carlos
Córdova-Lepe, Fernando
Velásquez, Nelson
Fecha
2022Resumen
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.
Fuente
Mathematics, 10(19), 3485Link de Acceso
Click aquí para ver el documentoIdentificador DOI
doi.org/10.3390/math10193485Colecciones
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