  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.
