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首页> 外文期刊>Journal of difference equations and applications >Global asymptotical stability of the positive equilibrium of a logistic competitive model
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Global asymptotical stability of the positive equilibrium of a logistic competitive model

机译：Logistic竞争模型的正平衡的全局渐近稳定性

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摘要

Global asymptotical stability of the positive equilibrium (PE) of a dynamical system is one of the research focus in theoretical studies of both continuous and discrete bio-mathematical models. In this paper, we shall establish the global asymptotical stability of the PE of a discrete Logistic competitive model in certain planar region. Indeed, sufficient conditions, dependent only on the parameters of the model, are obtained to ensure the global asymptotical stability of the PE in this region. The parameter region that corresponds to these sufficient conditions can be illustrated graphically and several examples of such regions are presented. Our approach to establish the global asymptotical stability of the PE involves proving the global attractivity of the PE in the planar region concerned and a key process here is the derivation of the maxima of the related functions in the planar region.
机译：动力学系统的正平衡（PE）的全局渐近稳定性是连续和离散生物数学模型理论研究的重点之一。在本文中，我们将建立离散Logistic竞争模型在一定平面区域内PE的全局渐近稳定性。确实，获得了仅取决于模型参数的充分条件，以确保该区域内PE的全局渐近稳定性。可以用图形说明与这些足够条件相对应的参数区域，并提供此类区域的几个示例。我们建立PE的全局渐近稳定性的方法涉及证明PE在有关平面区域中的全局吸引力，而此处的关键过程是推导平面区域中相关功能的最大值。

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