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Global Stability in Dynamical Systems with Multiple Feedback Mechanisms

机译:具有多重反馈机制的动力学系统的全局稳定性

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A class of n-dimensional ODEs with up to n feedbacks from the n’th variable is analysed. The feedbacks are represented by non-specific, bounded, non-negative C1 functions. The main result is the formulation and proof of an easily applicable criterion for existence of a globally stable fixed point of the system. The proof relies on the contraction mapping theorem. Applications of this type of systems are numerous in biology, e.g., models of the hypothalamic-pituitary-adrenal axis and testosterone secretion. Some results important for modelling are: 1) Existence of an attractive trapping region. This is a bounded set with non-negative elements where solutions cannot escape. All solutions are shown to converge to a “minimal” trapping region. 2) At least one fixed point exists. 3) Sufficient criteria for a unique fixed point are formulated. One case where this is fulfilled is when the feedbacks are negative.
机译:分析一类n维ODE,其中n个变量最多提供n个反馈。反馈由非特定的,有界的,非负的C1函数表示。主要结果是为系统的全局稳定定点的存在制定了易于应用的标准并对其进行了证明。证明依赖于收缩映射定理。这种类型的系统在生物学中的应用很多,例如下丘脑-垂体-肾上腺轴和睾丸激素分泌的模型。对于建模而言重要的一些结果是:1)存在诱人的诱集区域。这是具有非负元素的有界集合,其中解决方案无法逃脱。显示所有解决方案都收敛到“最小”陷印区域。 2)至少存在一个固定点。 3)制定了唯一定点的充分标准。做到这一点的一种情况是反馈为负。

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