Title :
Kuramoto model on smooth curved surfaces of high-dimensional spaces
Author_Institution :
Sch. of Math. Sci., Nanjing Normal Univ., Nanjing, China
Abstract :
In this paper, a high-dimensional Kuramoto model limited on smooth curved surfaces is established. A necessary and sufficient condition of equilibria is obtained and the linearized system around an equilibrium is derived. As the considered smooth curved surface is an ellipsoid, some dynamical properties including limit behavior and instability are obtained. Based on those results, almost global synchronization is achieved. Moreover, numerical simulations are given to validate the obtained theoretical results.
Keywords :
graph theory; linear systems; nonlinear control systems; stability; synchronisation; dynamical properties; equilibrium; global synchronization; high-dimensional Kuramoto model; high-dimensional spaces; instability; limit behavior; linearized system; necessary condition; numerical simulations; smooth curved surfaces; sufficient condition; Biological system modeling; Eigenvalues and eigenfunctions; Ellipsoids; Mathematical model; Symmetric matrices; Synchronization; Vectors; high-dimensional Kuramoto model; instability; synchronization;
Conference_Titel :
Control Conference (CCC), 2014 33rd Chinese
Conference_Location :
Nanjing
DOI :
10.1109/ChiCC.2014.6895940