Allee effect with time-varying migration on heterogeneous graphs

Takashi Nagatani, Genki Ichinose and Yuki Katsumata

Physica A: Statistical Mechanics and its Applications, 2019, vol. 527, issue C

Abstract: The behavior of animals during day and night can be demonstrated as time-varying migration. We study the effect of the temporal migration in a diffusively coupled Allee model on heterogeneous graphs. We present the metapopulation dynamic model for temporally heterogeneous graphs using the Allee effect of mobile individuals. We consider the small graphs with three and four nodes, and the star graphs with N nodes. A subpopulation (patch) is represented by a node on a graph. A link represents a temporal migration path between subpopulations. Mobile individuals move temporally by random walk through a link between nodes. Individuals grow or die out according to the Allee population dynamics within each subpopulation. The population dynamics in the metapopulation model are presented by reaction–diffusion equations with time-dependent diffusion coefficients. To evaluate the population size of each subpopulation (node), we obtain the solutions of the reaction–diffusion equations numerically for the small graphs and star graphs. The temporal migration path induces complex behavior for the Allee dynamics. The period (the inverse of frequency) of this temporal path has an important effect on the Allee dynamics.

Keywords: Networks; Allee effect; Random walk; Metapopulation; Temporal graph; Graph topology (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:527:y:2019:i:c:s0378437119307423

DOI: 10.1016/j.physa.2019.121276

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