Persistence and global stability in a delayed Leslie-Gower type three species food chain

Journal of Mathematical Analysis and Applications 340(1)

Nindjin A.F. and Aziz-Alaoui M.A.

Journal of Mathematical Analysis and Applications 340(1), pp. 340-357 (2008).

Article available online via the following DOI link : http://dx.doi.org/10.1016/j.jmaa.2007.07.078


Labo. of Applied Maths., EA 3821, Le Havre University, France.

Abstract

Our investigation concerns the three-dimensional delayed continuous time dynamical system which models a predator\u2013prey food chain. This model is based on the Holling-type II and a Leslie\u2013Gower modified functional response. This model can be considered as a first step towards a tritrophic model (of Leslie\u2013Gower and Holling\u2013Tanner 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.

Keywords: Time delay; Boundedness; Uniform persistence; Global stability; Lyapunov functional

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