中文摘要：

韵律行为是生物学上的一种普遍现象．这种行为相应于物理学上的回声波．该文给出了回声波的一般理论．具体地说，我们研究了一类典型的线性耦合系统的动力学行为，找到了回声波的形成机制，研究了回声波的稳定性并给出了一个判定稳定性的标准．为了应用本文所获得的理论结果，我们还给出了几个数值例子．

英文摘要：

The rhythmical behavior is a pervasive biological phenomenon. Such a behavior corresponds to echo wave in physics. This paper aims to present a general theory for the echo wave. Specifically, the dynamical behavior in a general coupled - linearly system is investigated, and a formation mechanism for echo waves is found. In addition, stability of echo waves and the corresponding criterion are obtained. These theoretical results can be straightforward applied to an arbitrarily special example. Numerical examples are used to verify the theoretical analysis.