General conditions for global stability in a single species population-toxicant model |
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| Institution: | 1. Laboratoire de Biologie Marine, Université Libre de Bruxelles, Avenue F.D.Roosevelt, 50. CP 160/15. 1050 BRUXELLES, BELGIUM;2. UMR 6282 Biogéosciences, Univ. Bourgogne Franche-Comté, CNRS, EPHE, 6 bd Gabriel F-21000 Dijon, France;3. British Antarctic Survey, Natural Environment Research Council, Cambridge, CB30ET UK;4. Kvaplan-Niva, Fram High North Research Centre for Climate and the Environment, 9296 Tromsø, Norway;5. Department of Theoretical Biology, VU University Amsterdam, de Boelelaan 1087, 1081 HV Amsterdam, The Netherlands |
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| 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 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 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. |
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