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Global dynamics of a nonlocal delayed reaction–diffusion equation on a half plane

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Abstract

We consider a delayed reaction–diffusion equation with spatial nonlocality on a half plane that describes population dynamics of a two-stage species living in a semi-infinite environment. A Neumann boundary condition is imposed accounting for an isolated domain. To describe the global dynamics, we first establish some a priori estimate for nontrivial solutions after investigating asymptotic properties of the nonlocal delayed effect and the diffusion operator, which enables us to show the permanence of the equation with respect to the compact open topology. We then employ standard dynamical system arguments to establish the global attractivity of the nontrivial equilibrium. The main results are illustrated by the diffusive Nicholson’s blowfly equation and the diffusive Mackey–Glass equation.

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Authors and Affiliations

  1. The Journal House, Hunan Normal University, Changsha, 410081, Hunan, People’s Republic of China

    Wenjie Hu

  2. School of Mathematics and Statistics, Central South University, Changsha, 410083, Hunan, People’s Republic of China

    Wenjie Hu & Yueliang Duan

Authors
  1. Wenjie Hu
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  2. Yueliang Duan
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Correspondence to Wenjie Hu.

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Hu, W., Duan, Y. Global dynamics of a nonlocal delayed reaction–diffusion equation on a half plane. Z. Angew. Math. Phys. 69, 26 (2018). https://doi.org/10.1007/s00033-018-0919-8

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  • DOI: https://doi.org/10.1007/s00033-018-0919-8

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