Abstract In this paper, firstly, we study the structural form of reflective integral for a given system. Then the sufficient conditions are obtained to ensure there exists the reflective integral with these structured form for such system. Secondly, we discuss the necessary conditions for the equivalence of such systems and a general three-dimensional differential system. And then, we apply the obtained results to the study of the behavior of their periodic solutions when such systems are periodic systems in t.

中文翻译：

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关于三维微分系统的等价性

摘要 本文首先研究了给定系统反射积分的结构形式。然后得到充分条件以保证这种系统存在与这些结构形式的反射积分。其次，我们讨论了这种系统与一般三维微分系统等价的必要条件。然后，我们将获得的结果应用于当这些系统是 t 中的周期系统时它们周期解的行为的研究。