振荡和可激发单位之间的合作行为：正耦合频率相关的特殊作用
Cooperative behavior between oscillatory and excitable units: the peculiar role of positive coupling-frequency correlations
摘要：
我们研究噪声驱动的可激发元素，所谓的主动旋转体的集体动力学。这里至关重要的是，固有频率和各个耦合强度是从一些联合概率分布中得出的。将平均场处理与高斯近似相结合，使我们能够找到无限维系统被简化为几个常微分方程的例子。我们的重点在于合作行为的人口组成的两个部分，其中一个是由可兴奋的元素，而另一个只包含自振荡单元。令人惊讶的是，整个系统中的可激发行为只有在可激发元件的耦合强度小于自振荡单元的耦合强度时才会发生。通过这种方式，固有频率和耦合之间的正的局部相关性塑造了可激发和振荡元素的混合群体的全局行为。
英文摘要：
We study the collective dynamics of noise-driven excitable elements, so-called active rotators. Crucially here, the natural frequencies and the individual coupling strengths are drawn from some joint probability distribution. Combining a mean-field treatment with a Gaussian approximation allows us to find examples where the infinite-dimensional system is reduced to a few ordinary differential equations. Our focus lies in the cooperative behavior in a population consisting of two parts, where one is composed of excitable elements, while the other one contains only self-oscillatory units. Surprisingly, excitable behavior in the whole system sets in only if the excitable elements have a smaller coupling strength than the self-oscillating units. In this way positive local correlations between natural frequencies and couplings shape the global behavior of mixed populations of excitable and oscillatory elements.
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