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- W2070107099 abstract "This manuscript is devoted to the study of some spreading properties of Holling–Tanner prey–predator reaction–diffusion system. We more particularly focus on the invasion of introduced predator in some environment which is initially well-populated of prey. We first prove that, for the arbitrary dimensional problem, the system has a spreading speed property. We derive more precise information for the one-dimensional system for which the long time behaviour is studied and it is proved that the solution converges (in some sense) towards a generalized transition wave with some determined global mean speed of propagation. Dans cet article on étudie lʼinvasion dʼun prédateur introduit dans un environment spatial homogonène riche en proie. Le modèle mathématique consideré est un système de réaction–diffusion posé dans tout lʼespace avec des interactions proies–prédateurs de type Holling–Tanner. Dans un premier temps, sans faire dʼhypothèse sur la dimension de lʼespace, on caractérise la zone dʼexpansion de la population de prédateurs. Une étude plus approfondie est ensuite menée dans le cadre monodimensionnel en espace. Dans ce cas, on montre que le comportement asymptotique des solutions est décrit par des ondes de transition généralisées dont la vitesse moyenne est explicitée en fonction des paramètres du modèle." @default.
- W2070107099 created "2016-06-24" @default.
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- W2070107099 date "2013-07-01" @default.
- W2070107099 modified "2023-09-25" @default.
- W2070107099 title "Convergence to generalized transition waves for some Holling–Tanner prey–predator reaction–diffusion system" @default.
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- W2070107099 doi "https://doi.org/10.1016/j.matpur.2012.10.009" @default.
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