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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.

MSC:

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