TY - JOUR
T1 - Synchronization of weighted networks and complex synchronized regions
AU - Duan, Zhisheng
AU - Chen, Guanrong
AU - Huang, Lin
PY - 2008/5/19
Y1 - 2008/5/19
N2 - Since the Laplacian matrices of weighted networks usually have complex eigenvalues, the problem of complex synchronized regions should be investigated carefully. The present Letter addresses this important problem by converting it to a matrix stability problem with respect to a complex parameter, which gives rise to several types of complex synchronized regions, including bounded, unbounded, disconnected, and empty regions. Because of the existence of disconnected synchronized regions, the convexity characteristic of stability for matrix pencils is further discussed. Then, some efficient methods for designing local feedback controllers and inner-linking matrices to enlarge the synchronized regions are developed and analyzed. Finally, a weighted network of smooth Chua's circuits is presented as an example for illustration. © 2008 Elsevier B.V. All rights reserved.
AB - Since the Laplacian matrices of weighted networks usually have complex eigenvalues, the problem of complex synchronized regions should be investigated carefully. The present Letter addresses this important problem by converting it to a matrix stability problem with respect to a complex parameter, which gives rise to several types of complex synchronized regions, including bounded, unbounded, disconnected, and empty regions. Because of the existence of disconnected synchronized regions, the convexity characteristic of stability for matrix pencils is further discussed. Then, some efficient methods for designing local feedback controllers and inner-linking matrices to enlarge the synchronized regions are developed and analyzed. Finally, a weighted network of smooth Chua's circuits is presented as an example for illustration. © 2008 Elsevier B.V. All rights reserved.
KW - Complex synchronized region
KW - Matrix pencil
KW - Network synchronization
KW - Weighted network
UR - http://www.scopus.com/inward/record.url?scp=42749089467&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-42749089467&origin=recordpage
U2 - 10.1016/j.physleta.2008.02.056
DO - 10.1016/j.physleta.2008.02.056
M3 - 21_Publication in refereed journal
VL - 372
SP - 3741
EP - 3751
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
SN - 0375-9601
IS - 21
ER -