TY  - JOUR
A1  - Motter, Adilson E.
A1  - Zhou, Changsong
A1  - Kurths, Jürgen
T1  - Enhancing complex-network synchronization
N2  - Heterogeneity in the degree (connectivity) distribution has been shown to suppress synchronization in networks of symmetrically coupled oscillators with uniform coupling strength (unweighted coupling). Here we uncover a condition for enhanced synchronization in weighted networks with asymmetric coupling. We show that, in the optimum regime, synchronizability is solely determined by the average degree and does not depend on the system size and the details of the degree distribution. In scale-free networks, where the average degree may increase with heterogeneity, synchronizability is drastically enhanced and may become positively correlated with heterogeneity, while the overall cost involved in the network coupling is significantly reduced as compared to the case of unwcighted coupling
Y1  - 2005
SN  - 0295-5075
ER  - 
TY  - JOUR
A1  - Motter, Adilson E.
A1  - Zhou, Changsong
A1  - Kurths, Jürgen
T1  - Network synchronization, diffusion, and the paradox of heterogeneity
N2  - Many complex networks display strong heterogeneity in the degree (connectivity) distribution. Heterogeneity in the degree distribution often reduces the average distance between nodes but, paradoxically, may suppress synchronization in networks of oscillators coupled symmetrically with uniform coupling strength. Here we offer a solution to this apparent paradox. Our analysis is partially based on the identification of a diffusive process underlying the communication between oscillators and reveals a striking relation between this process and the condition for the linear stability of the synchronized states. We show that, for a given degree distribution, the maximum synchronizability is achieved when the network of couplings is weighted and directed and the overall cost involved in the couplings is minimum. This enhanced synchronizability is solely determined by the mean degree and does not depend on the degree distribution and system size. Numerical verification of the main results is provided for representative classes of small-world and scale-free networks
Y1  - 2005
SN  - 1063-651X
ER  - 
TY  - JOUR
A1  - Zhou, Changsong
A1  - Motter, Adilson E.
A1  - Kurths, Jürgen
T1  - Universality in the synchronization of weighted random networks
N2  - Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in the connection strengths. Here we study synchronization in weighted complex networks and show that the synchronizability of random networks with a large minimum degree is determined by two leading parameters: the mean degree and the heterogeneity of the distribution of node's intensity, where the intensity of a node, defined as the total strength of input connections, is a natural combination of topology and weights. Our results provide a possibility for the control of synchronization in complex networks by the manipulation of a few parameters
Y1  - 2006
UR  - http://prl.aps.org/pdf/PRL/v96/i3/e034101
U6  - https://doi.org/10.1103/Physrevlett.96.034101
ER  - 
TY  - GEN
A1  - Motter, Adilson E.
A1  - Matias, Manuel A.
A1  - Kurths, Jürgen
A1  - Ott, Edward
T1  - Dynamics on complex networks and applications
T2  - Physica. D, Nonlinear phenomena
KW  - complex systems
KW  - nonlinear dynamics
KW  - statistical physics
Y1  - 2006
U6  - https://doi.org/10.1016/j.physd.2006.09.012
SN  - 0167-2789
VL  - 224
IS  - 1-2
SP  - VII
EP  - VIII
PB  - Elsevier
CY  - Amsterdam
ER  -