Abstract
We study the large time behavior of a class of diffusive predator–prey systems posed on the whole Euclidean space. By studying a family of similar problems with all possible spatial translations, we first prove the asymptotic persistence of the prey for the spatially heterogeneous case under certain assumptions on the coefficients. Then, applying this persistence theorem, we prove the convergence of the solution to the unique positive equilibrium for the spatially homogeneous case, under certain restrictions on the space dimension and the predation coefficient.
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J.-S. Guo is partially supported by the Ministry of Science and Technology of Taiwan under the Grant 102-2115-M-032-003-MY3. Part of this work was carried out during a visit of the A. Ducrot to Tamkang University. We would like to thank the support of the National Center for Theoretic Sciences for his visit.
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Ducrot, A., Guo, JS. Asymptotic behavior of solutions to a class of diffusive predator–prey systems. J. Evol. Equ. 18, 755–775 (2018). https://doi.org/10.1007/s00028-017-0418-y
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DOI: https://doi.org/10.1007/s00028-017-0418-y