Asymptotic behavior of nonlinear compartmental systems: Nonoscillation and stability
Asymptotic behavior of nonlinear compartmental systems: Nonoscillation and stability
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非线性隔室系统的渐近行为：不振荡和稳定性
DOI：
10.1109/tcs.1978.1084490
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发表时间：
1978
期刊：
影响因子：
--
通讯作者：
Y. Ohta
中科院分区：
文献类型：
--
作者：
H. Maeda;S. Kodama;Y. Ohta
本文讨论了一类非线性分区系统的稳定性。具体而言，数学条件，保证相同的定性行为固有的线性房室系统被认为是。我们首先考虑解的非振动性，并证明在较温和的条件下该系统不存在周期振动。然后，使用的结果来推导出一个必要和充分的条件，每个解决方案，以收敛到一组可能取决于输入和初始状态的均衡点。给出了平衡态仅依赖于输入的一个充分条件。研究了自由系统的渐近性态，给出了原点全局渐近稳定的充分条件。此外，对于一个封闭的房室系统，它表明，对于每个给定的初始状态，唯一的平衡状态，如果它存在，只依赖于初始状态的组件的总和。最后给出了解收敛到唯一点的一个充分条件。
This paper discusses properties related to the stability of a class of nonlinear compartmental systems. Specifically, mathematical conditions which guarantee the same qualitative behavior inherent in linear compartmental systems are considered. We first consider the nonoscillatory property of solutions and show that the system has no periodic oscillation under a mild condition. The result is then used to derive a necessary and sufficient condition for every solution to converge to a set of equlibrium points which may depend both on the input and the initial state. A sufficient condition is also given for an equilibrium state to depend only on the input. The asymptotic behavior of the free systems is also considered, and a sufficient condition is given for the origin to be globally asymptotically stable. Furthermore, for a closed compartmental system it is shown that for each given initial state, unique equilibrium state, if it exists, depends only on the total sum of the components of the initial state. Finally a sufficient condition is given for solutions to converge to the unique point.