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Cooperative behavior between oscillatory and excitable units: the peculiar role of positive coupling-frequency correlations

Research paper by Bernard Sonnenschein, Thomas K. DM. Peron, Francisco A. Rodrigues, Jürgen Kurths, Lutz Schimansky-Geier

Indexed on: 15 Aug '14Published on: 15 Aug '14Published in: Physics - Disordered Systems and Neural Networks



Abstract

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.