Excitable systems are a class of dynamical systems that can generate self-sustaining waves of activity. These waves are known to manifest differently under diverse conditions, whereas some travel as planar or radial waves, and others evolve into rotating spirals. Excitable systems can also form stationary stable patterns through standing waves. Under certain conditions, these waves are also known to be reflected at no-flux boundaries. Here, we review the basic characteristics of these four entities: traveling, rotating, standing and reflected waves. By studying their mechanisms of formation, we show how through manipulation of three critical parameters: time-scale separation, space-scale separation and threshold, we can interchangeably control the formation of all the aforementioned wave types.

中文翻译：

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通过调整三个参数来控制可激波行为。

兴奋性系统是一类可以产生自我维持的活动波的动力系统。众所周知，这些波在不同条件下会表现出不同的形式，而有些则以平面波或径向波传播，而另一些则演变成旋转螺旋。激励系统还可以通过驻波形成平稳的稳定模式。在某些情况下，也已知这些波会在无磁通边界处反射。在这里，我们回顾了这四个实体的基本特征：行进，旋转，驻波和反射波。通过研究它们的形成机理，我们展示了如何通过操纵三个关键参数：时间尺度分离，空间尺度分离和阈值，可以互换地控制所有上述波浪类型的形成。