Berlin 2018 – scientific programme
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SOE: Fachverband Physik sozio-ökonomischer Systeme
SOE 16: Networks: From Topology to Dynamics (joint session DY/SOE)
SOE 16.7: Talk
Wednesday, March 14, 2018, 17:15–17:30, MA 001
Self-consistent correlations of randomly coupled rotators in the asynchronous state — •Alexander van Meegen1,2,3 and Benjamin Lindner1,2 — 1Humboldt Universität zu Berlin — 2Bernstein Zentrum Berlin — 3Forschungszentrum Jülich
We present a study of a network of unidirectionally coupled rotators with i.i.d. frequencies and i.i.d. coupling coefficients. Similar to biological networks, this system can attain an asynchronous state with pronounced temporal autocorrelations of the rotators.
Using an approach based on the system's generating functional, we derived a differential equation for the self-consistent autocorrelation function of the network noise. Its numerical solution has been confirmed by simulations of networks with Gaussian or sparsely distributed coupling coefficients. Explicit expressions for correlation function, power spectra, correlation time, noise intensity, and quality factor for the case of identical frequencies for all rotators in the limits of weak or strong coupling strength have been obtained.
This work paves the way for more detailed studies of how the statistics of connection strength, the heterogeneity of network parameters, and the form of the interaction function shape the network noise and the autocorrelations of the single element if this element has an predominantly oscillatory nature (e.g. a limit-cycle system).