Cooperative behavior between oscillatory and excitable units: the   peculiar role of positive coupling-frequency correlations
  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. 
Bernard Sonnenschein, Thomas K. DM. Peron, Francisco A. Rodrigues,   J\"urgen Kurths, Lutz Schimansky-Geier
cond-mat.dis-nn cond-mat.stat-mech nlin.CD physics.bio-ph