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- W4311767461 abstract "In this paper, we study the propagation dynamics of a time-periodic predator-prey system with nonlocal dispersal. We first establish the existence and nonexistence of periodic traveling waves and then investigate the spreading properties of solutions starting from compactly supported initial conditions. Roughly speaking, we show that if predators disperse faster than the prey, then both species spread simultaneously; whereas if the prey disperses faster than predators, then there exist two separate invasion fronts, one front occurs as the prey invades open habitats, and the other front appears when predators catch up the prey. We emphasize that one needs to find some new techniques to treat nonlocal predator-prey systems due to the presence of the time dependence of nonlinearity, the lack of compactness of the nonlocal dispersal operators and the lack of the comparison principle for predator-prey systems. Dans cet article, nous étudions la dynamique de propagation pour un système prédateur-proie périodique en temps avec une dispersion non-locale. Nous étudions d'abord l'existence et inexistence des ondes progressives périodiques et nous étudions ensuite la propriété de propagation des solutions à partir de conditions initiales à supports compactes. Nous montrons que si les prédateurs se dispersent plus rapidement que la proie, alors les deux espèces se sont propagées simultanément ; tandis que si la proie se disperse plus vite que les prédateurs, alors il existe deux fronts d'invasion séparés, un front se produit lorsque la proie envahit les habitats ouverts et l'autre front apparaît lorsque les prédateurs rattrapent la proie. Nous soulignons qu'il faut trouver de nouvelles techniques pour traiter les systèmes prédateur-proie non-locaux en raison de la présence de la dépendance temporelle de la non-linéarité, le manque de compacité des opérateurs de dispersion non-locale et l'absence de principe de comparaison pour les systèmes prédateur-proie." @default.
- W4311767461 created "2022-12-28" @default.
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- W4311767461 date "2023-02-01" @default.
- W4311767461 modified "2023-10-16" @default.
- W4311767461 title "Propagation dynamics in periodic predator-prey systems with nonlocal dispersal" @default.
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- W4311767461 doi "https://doi.org/10.1016/j.matpur.2022.12.003" @default.
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