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 :
Labo. of Applied Maths., EA 3821,
Le Havre University, France.
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
Keywords: Time delay; Boundedness; Uniform persistence; Global stability; Lyapunov functional
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