中文摘要：

Since 1974,studying the original delay differential equation given by Kaplan and Yorke is about the problem on the existence of its periodic solutions,there have been a series of interesting and significant results in the previous literature.In this paper,we present a survey of some basic results.Some interesting open problems are also addressed.

英文摘要：

Since 1974, studying the original delay differential equation given by Kaplan and Yorke is about the problem on the existence of its periodic solutions, there have been a series of interesting and significant results in the previous literature. In this paper, we present a survey of some basic results. Some interesting open problems are also