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Allee effect with time-varying migration on heterogeneous graphs

Author

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  • Nagatani, Takashi
  • Ichinose, Genki
  • Katsumata, Yuki

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.

Suggested Citation

  • Nagatani, Takashi & Ichinose, Genki & Katsumata, Yuki, 2019. "Allee effect with time-varying migration on heterogeneous graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 527(C).
    • Handle: RePEc:eee:phsmap:v:527:y:2019:i:c:s0378437119307423
    DOI: 10.1016/j.physa.2019.121276
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    Cited by:

    1. Nagatani, Takashi, 2020. "Traffic flow on percolation-backbone fractal," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    2. Nagatani, Takashi, 2021. "Traffic flow on star graph: Nonlinear diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).

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