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Asymptotic pattern of a migratory and nonmonotone population model

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  • In this paper, we consider a time-delayed and nonlocal population model with migration and relax the monotone assumption for the birth function. We study the global dynamics of the model system when the spatial domain is bounded. If the spatial domain is unbounded, we investigate the spreading speed $c^*$, the non-existence of traveling wave solutions with speed $c\in(0,c^*)$, the existence of traveling wave solutions with $c\geq c^*$, and the uniqueness of traveling wave solutions with $c>c^*$. It is shown that the spreading speed coincides with the minimal wave speed of traveling waves.
    Mathematics Subject Classification: Primary: 35K57, 35B40; Secondary: 92B05.

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