On the dynamics of predator-prey models
with a modified Holling-Tanner functionnal response
M. Daher Okiye and M. A. Aziz-Alaoui
Labo. Applied Math., Le Havre University
Proc. Mathematical Modelling and Computing in Biology
and Medecine, pp: 270-278.
ESMTB 5th Intern. Conf. (ECMTB'2002),
Milano, Italy, July 2-6, 2002.
Dynamic behavior of a two-dimensionnal system modeling a
predator-prey food chain with modified Holling-Tanner
scheme is analyzed into two parts.
In the first one, we study the system without diffusion
(with no-flux boundary conditions).
We establish assumptions under which we have boundedness of
solutions, existence of a positively invariant and
attrating set, the global stability of the
coexisting interior equilibrum via a Lyapunov fonction,
and, finally, the exitence of limit cycles is discussed.
In the second part, we study the system with term of
We introduce criteria for permanence (uniform persistence
Back to the previous page
Back to Aziz Alaoui's home page