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General conditions for global stability in a single species population-toxicant model

机译:单一物种种群毒性模型中全球稳定性的一般条件

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摘要

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. (C) 2004 Elsevier Ltd. All rights reserved.
机译:我们以众所周知的人口有毒物质模型处理全球稳定问题。我们使用几何方法对常微分方程进行全局稳定性分析,该方法基于对Bendixson准则的高阶推广。我们为唯一非平凡平衡的全局稳定性获得了充分的条件。这些条件用描述种群动态的通用功能表示。在类似logistic的人口动态的特殊情况下,我们得到了改善条件的条件,这些条件是通过Lyapunov直接方法获得的。 (C)2004 Elsevier Ltd.保留所有权利。

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