Abstract

A logistic equation with a delay depending on the state in the past is considered. We study the question of the existence of nonlocal relaxation periodic solutions of this equation for large values of the parameter. The characteristics (for example, period and extreme values) of solutions that we find are compared with similar characteristics of solutions of other modifications of this equation. Asymptotic estimates for the period and the maximum and minimum values are obtained. The study is carried out by the large parameter method.

中文翻译：

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具有过去状态相关延迟的逻辑方程中的松弛振荡

摘要

考虑具有依赖于过去状态的延迟的逻辑方程。我们研究了该方程的非局部松弛周期解对于大参数值是否存在的问题。将我们找到的解的特征（例如，周期和极值）与该方程的其他修改的解的相似特征进行比较。获得该周期的渐近估计以及最大值和最小值。研究采用大参数法。