2011/12/31 by Bernard Sonnenschein, Lutz Schimansky-Geier
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · #Gene Regulatory Network Analysis #Neural Networks Stability and Synchronization #Nonlinear Dynamics and Pattern Formation #cond-mat.dis-nn #nlin.CD #physics.bio-ph
paper · pdf · doi:10.1103/physreve.85.051116
published as Phys. Rev. E 85, 051116 (2012) · 20 pages, 10 figures, 1 table. Accepted for publication in Physical Review E
arxiv created 2012/05/02 · openalex publication_date 2012/05/14 · arxiv updated 2012/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We study networks of noisy phase oscillators whose nodes are characterized by random degrees counting the number of their connections. Both these degrees and the natural frequencies of the oscillators are distributed according to a given probability density. Replacing the randomly connected network by an all-to-all coupled network with weighted edges allows us to formulate the dynamics of a single oscillator coupled to the mean field and to derive the corresponding Fokker-Planck equation. From the latter we calculate the critical coupling strength for the onset of synchronization as a function of the noise intensity, the frequency distribution, and the first two moments of the degree distribution. Our approach is applied to a dense small-world network model, for which we calculate the degree distribution. Numerical simulations prove the validity of the replacement. We also test the applicability to more sparsely connected networks and formulate homogeneity and absence of correlations in the degree distribution as limiting factors of our approach.