Nonlinear Analysis:Real World Applications 5 (2004) 749–762 www.elsevier.com/locate/na General conditions for global stability in a single species population-toxicant model B. Buonomo a ; * , D. Lacitignola b a Department of Mathematics and Applications, University of Naples Federico II, via Cintia, I-80126 Naples, Italy b Department of Mathematics, University of Lecce, via Provinciale Lecce-Arnesano, I-73100 Lecce, Italy Abstract 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 dierential equation which is based on the use of a higher-order generalization of the Bendixson’s criterion. We obtain sucient conditions for the global stability of the unique nontrivial 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. ? 2004 Elsevier Ltd. All rights reserved. Keywords: Population dynamics; Toxicants; Global stability; Compound matrices 1. Introduction Let T (t ), U (t ) and N (t ) represent at time t the concentration of toxicant in the environment, the concentration of the toxicant in the total population and the population biomass, respectively. Mass balance arguments drive to the following model:        ˙ T = Q -  0 T - NT + NU; ˙ U = NT -  1 U - NU; ˙ N = F(T; U; N ); (1) ∗ Corresponding author. E-mail addresses: buonomo@unina.it (B. Buonomo), deborah.lacitignola@unile.it (D. Lacitignola). 1468-1218/$-see front matter ? 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.nonrwa.2004.05.002