2019/02/04 by Claudio Maggi, Matteo Paoluzzi, Maggi, Claudio +1
Computer Science · Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Opinion Dynamics and Social Influence #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.1902.01247
openalex publication_date 2019/02/04 · openalex created_date 2019/10/10 · openalex updated_date 2026/07/28
Many natural and social phenomena are characterized by synchronization. The Kuramoto model, taking into account the basic ingredients for observing synchronized states, allows to study mathematically synchronization in a simplified but nontrivial picture. Here we study how a noise that is correlated on a finite time-scale τ impacts the ability of the Kuramoto model to achieve synchronization. We develop an approximated theory that allows to compute the critical coupling constant kc as a function of the correlation time τ. We obtain that that kc(τ) decreases as τ increases indicating that time-correlated noise promotes synchronization. Moreover, we show that theory describes qualitatively well the degree of synchronization near kc obtained numerically. Finally, we show that, independently on the value of τ, the curves of the order parameter versus k scale on the same master curve even at values of k very far from kc.