Investigating the synchronizability of complex networks
Abstract
There is a broad literature on the synchronization of networks of coupled dynamical systems. Within these works, an important proble,m is that of characterizing the stability of the synchronous solution. The popular definition of network synchronizability describes, the range of the coupling strength over which the the synchronous solution is stable. A separate, but perhaps more important proble,m, is the robustness of the synchronous solution to (large) perturbations. In the presence of a non-normal Laplacian matrix, which d,escribes the network connectivity, the modes of a stable network may couple and produce a transient dynamics (overshoot) that will d,epart from the synchronous state. It becomes therefore important to characterize this overshoot. We will first analyze this problem,using a simple network with only three oscillators. We will then generalize to a large network with manynodes. We will show that und,er certain conditions, the overshoot grows linearly with the degree of non-normality. We will attempt to come up with analytic chara,cterization and a numerical approximation for the overshoot, under the assumption that the eigenvalues of the Laplacian matrix are e,ither negative real part or zero. The PI and the graduate student will work on this important mathematical question and try to relat,e the overshoot to the degree of non-normality of the Laplacian matrix.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Sep 03, 2022
- Source ID
- N000142212766
Entities
People
- Francesco Sorrentino
Organizations
- Office of Naval Research
- United States Navy
- University of New Mexico