Global stability of a biological model with time delay
Global stability of a biological model with time delay
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DOI：
10.1090/s0002-9939-1986-0813814-3
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发表时间：
1986
期刊：
影响因子：
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通讯作者：
S. Lenhart;C. Travis
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文献类型：
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作者：
S. Lenhart;C. Travis
本文给出了一类logistic时滞微分方程全局稳定的充分必要条件。生物模型经常导致延迟微分方程和有关这种模型的平衡解的稳定性的问题。库欣(6)和麦克唐纳（16）的专著从种群动力学、生态学和生理学等方面讨论了许多这类模型的例子。这种模型的大部分工作都集中在延迟方程上，这些方程可以通过变量的变化而简化为无延迟的微分方程系统（3,4,8,14,18,19）。另一个研究方向是关于L x(t) = ax(t) +£btx(t - r,), r, > 0, /=i的线性延迟泛函微分方程对于延迟（1,3,5,7,9,11,12,14）的所有值渐近稳定的条件。我们建议将这些研究结合起来，并检查广泛使用的人口动态逻辑模型的全球稳定性，
This paper gives necessary and sufficient conditions for global stability of certain logistic delay differential equations for all values of the delay. Biological models frequently lead to delay differential equations and to questions concerning the stability of equilibrium solutions of such models. The monographs by Cushing (6) and MacDonald (16) discuss a number of examples of such models from population dynamics, ecology, and physiology. Much of the work with such models has focused on delay equations which are reducible, through a change of variables, to systems of differential equations without delays (3,4,8,14,18,19). Another line of research is concerned with conditions under which linear retarded functional differential equations of the form L x(t) = ax(t) + £ btx(t - r,), r, > 0, /=i are asymptotically stable for all values of the delay (1,3,5,7,9,11,12,14). We propose to combine these lines of research and examine global stability of the widely used logistic model of population dynamics,