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.

MIRIAM editions

ESMTB 5th Intern. Conf. (ECMTB'2002), Milano, Italy, July 2-6, 2002.

ABSTRACT

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 reaction-diffusion. We introduce criteria for permanence (uniform persistence and dissipativity).

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