The Delay Logistic Equation
The Delay Logistic Equation
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DOI：
10.1007/978-94-015-7920-9_1
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发表时间：
1992
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影响因子：
--
通讯作者：
K. Gopalsamy
中科院分区：
文献类型：
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作者：
K. Gopalsamy
在这一章中，我们研究了自治时滞微分方程及其几个变体的非常数正解的渐近性态，其中a，bj，τj（j= 1，2，…，n）为正常数。等式式（1.1.1）对应于r，τ，K为正数的一个等式的推广。哈钦森[1948]曾建议，（1.1.2）可以用来模拟具有恒定繁殖率的单一物种种群向饱和水平K增长的动力学;（1.1.2）中的项表示一种依赖于密度的反馈机制，它需要τ个单位的时间来响应（1.1.2）中用N表示的种群密度的变化。通过改变变量，（1.1.2）式可化为如下形式的方程其中α为正常数。等式（1.1.3）已经被许多作者研究过，特别是Kakutani和Markus [1958]，Jones [1962]和Wright [1955]。
In this chapter we are concerned with an investigation of the asymptotic behavior, ast→ ∞ of positive nonconstant solutions of the autonomous delay-differential equationand several of its variants wherea,bj, τj(j= 1,2,...,n) are positive constants. Eqn. (1.1.1) corresponds to a generalization of an equation of the formin whichr, τ,Kare positive numbers. It has been suggested by Hutchinson [1948] that (1.1.2) can be used to model the dynamics of a single species population growing towards a saturation levelKwith a constant reproduction rater; the term \[in (1.1.2) denotes a density dependent feedback mechanism which takes τ units of time to respond to changes in the population density represented in (1.1.2) byN. By a change of variables, (1.1.2) can be brought to an equation of the formwhere α is a positive constant. Eqn.(1.1.3) has been studied by numerous authors and notably, by Kakutani and Markus [1958], Jones [1962] and Wright [1955].