Synchronization in dynamical networks: evolution along commutative graphs
S Boccaletti1, D-U Hwang, M Chavez
1CNR-Istituto dei Sistemi Complessi, Largo E. Fermi 6, 50125 Florence, Italy.
Abstract:
Starting from an initial wiring of connections, we show that the synchronizability of a network can be significantly improved by evolving the graph along a time dependent connectivity matrix. We consider the case of connectivity matrices that commute at all times, and compare several approaches to engineer the corresponding commutative graphs. In particular, we show that synchronization in a dynamical network can be achieved even in the case in which each individual commutative graphs does not give rise to synchronized behavior.
Related Concept Videos
Graphs of Equations in Two Variables
Transmission-Line Differential Equations
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from the...
Sequence Networks of Rotating Machines
Zero-sequence current induces a voltage drop across the generator's neutral impedance and other...
Entropy Change in Reversible Processes
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
Graphs of Two-Variable Functions
BIBO stability of continuous and discrete -time systems
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.

