Bernard Sonnenschein, Michael A. Zaks, Alexander B. Neiman, Lutz Schimansky-Geier
We study collective dynamics of complex networks of stochastic excitable elements, active rotators. In the thermodynamic limit of infinite number of elements, we develop a mean-field theory for the network and then use a Gaussian approximation to obtain a closed sequence of deterministic integro-differential equations. These equations govern the order parameters of the network. We find that a homogeneous decrease in the number of elements connections merely shifts the bifurcation thresholds without producing qualitative changes in the network dynamics. In contrast, heterogeneity in the number of connections leads to bifurcations in the excitable regime. In particular we show that a critical value of noise intensity for the saddle-node bifurcation decreases with growing connectivity variance. The threshold values of noise intensity for the onset of global oscillations (Hopf bifurcation) show a non-monotone dependency on the structural heterogeneity, displaying a minimum at moderate connectivity variances.
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http://arxiv.org/abs/1305.0197
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