2013/03/12 by Marcos D. N. Maia, Maia, Marcos D. N.
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Optical Network Technologies #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Quantum optics and atomic interactions #Slime Mold and Myxomycetes Research #math.DS
paper · pdf · doi:10.48550/arxiv.1303.3019
72 pages, 13 figures, text in Portuguese
arxiv created 2013/03/12 · openalex publication_date 2013/03/12 · arxiv updated 2013/03/14 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
We investigate emergence of the global collective behavior in networks of diffusively coupled identical oscillators, which in the established model is an invariant manifold of the motion equations. The interaction is modeled with the graph theory and dynamical systems theory. We use the uniform contractions theory in non-autonomous linear differential equations to address the criterion under the global coupling parameter, which it turns defines the synchronized motion and it stability under small linear and non-linear perturbations. The critical global interaction parameter is given only by the isolated dynamics, by the spectral properties of the coupling function and the second eigenvalue network laplacian.