Persistence and global stability in a delayed Leslie-Gower type three species food chain |
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Authors: | AF Nindjin |
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Institution: | a Laboratoire de Mathématiques Appliquées, Université de Cocody, 22 BP 582, Abidjan 22, Côte d'Ivoire b Laboratoire de Mathématiques Appliquées, Université du Havre, 25 rue Philippe Lebon, BP 540, 76058 Le Havre Cedex, France |
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Abstract: | Our investigation concerns the three-dimensional delayed continuous time dynamical system which models a predator-prey food chain. This model is based on the Holling-type II and a Leslie-Gower modified functional response. This model can be considered as a first step towards a tritrophic model (of Leslie-Gower and Holling-Tanner type) with inverse trophic relation and time delay. That is when a certain species that is usually eaten can consume immature predators. It is proved that the system is uniformly persistent under some appropriate conditions. By constructing a proper Lyapunov function, we obtain a sufficient condition for global stability of the positive equilibrium. |
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Keywords: | Time delay Boundedness Uniform persistence Global stability Lyapunov functional |
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