General global stability conditions for a class of ODE modelling population-toxicant interactions.
by
Bruno Buonomo
Department of Mathematics and Applications. University of Naples Federico II. via Cintia. I-80126 Naples, Italy
Coauthors: Deborah Lacitignola. Department of Mathematics. University of Lecce. via Provinciale Lecce-Arnesano. I-73100 Lecce, Italy.

We deal with the global stability for a well known population-toxicant model. We make use of a geometrical approach to the global stability analysis for ordinary differential equation which is based on the use of a higher-order generalization of the Bendixson's criterion. We obtain sufficient conditions for the global stability of the unique non-trivial equilibrium. These conditions are expressed in terms of a generic functional describing the population dynamics. In the special case of a logistic-like population dynamics, we get conditions which improve the ones previously known, obtained by means of the Lyapunov direct method.

Date received: February 25, 2003