论文标题
使用符号Euler的方法保证混合振荡器的相位同步：Brusselator和Biped示例
Guaranteed phase synchronization of hybrid oscillators using symbolic Euler's method: The Brusselator and biped examples
论文作者
论文摘要
在17世纪，霍根斯（Huygens）证明了相同步的现象，同时观察到两个倾斜的时钟摆在同一壁上。最近，这种现象本质上是一种广泛的现象，事实证明有多种工业应用。但是，该现象本身表现出的系统的确切参数值通常是微妙的，因此找到正式的足够条件以保证相同步。使用可及性的概念，我们在这里给出了一种正式的方法。更确切地说，我们的方法选择了状态空间的一部分$ s $，并表明以$ s $开头的任何解决方案均在固定数量的$ k $中返回到$ s $。此外，我们的方法表明溶液的组成部分是（几乎）相相。我们解释了该方法如何应用于Brusselator反应扩散和Biped Walker示例。
The phenomenon of phase synchronization was evidenced in the 17th century by Huygens while observing two pendulums of clocks leaning against the same wall. This phenomenon has more recently appeared as a widespread phenomenon in nature, and turns out to have multiple industrial applications. The exact parameter values of the system for which the phenomenon manifests itself are however delicate to obtain in general, and it is interesting to find formal sufficient conditions to guarantee phase synchronization. Using the notion of reachability, we give here such a formal method. More precisely, our method selects a portion $S$ of the state space, and shows that any solution starting at $S$ returns to $S$ within a fixed number of periods $k$. Besides, our method shows that the components of the solution are then (almost) in phase. We explain how the method applies on the Brusselator reaction-diffusion and the biped walker examples.
