Abstract

A logistic delay equation with diffusion, which is important in applications, is studied. It is assumed that all of its coefficients, as well as the coefficients in the boundary conditions, are rapidly oscillating functions of time. An averaged equation is constructed, and the relation between its solutions and the solutions of the original equation is studied. A result on the stability of the solutions is formulated, and the problem of local dynamics in the critical case is studied. An algorithm for constructing the asymptotics of the solutions and an algorithm for studying their stability are proposed. It is important to note that the corresponding algorithm contains both a regular and a boundary layer component. Meaningful examples are given.

中文翻译：

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具有扩散和快速振荡系数的逻辑时滞方程的Andronov-Hopf分支

摘要

研究了在应用中很重要的具有扩散的逻辑时滞方程。假定其所有系数以及边界条件下的系数都是时间的快速振荡函数。构造一个平均方程，研究其解与原始方程解之间的关系。提出了解决方案稳定性的结果，并研究了临界情况下的局部动力学问题。提出了构造渐近性的算法和研究其稳定性的算法。重要的是要注意，相应的算法既包含常规层又包含边界层部分。给出了有意义的例子。