General conditions for global stability in a single species population-toxicant model. (English) Zbl 1074.92036

Summary: 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 equations which is based on the use of a higher-order generalization of the Bendixson criterion. We obtain sufficient 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 logistic-like population dynamics, we get conditions which improve the ones previously known, obtained by means of the Lyapunov direct method.


92D40 Ecology
34D23 Global stability of solutions to ordinary differential equations
92D25 Population dynamics (general)
Full Text: DOI


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