Stability of non-diagonalizable networks: Eigenvalue analysis

Linying Xiang; Zengqiang Chen; Jonathan J.H. Zhu

doi:10.1007/978-3-642-02466-5_98

Stability of non-diagonalizable networks: Eigenvalue analysis

Linying Xiang^*
, Zengqiang Chen
, Jonathan J.H. Zhu

^*Corresponding author for this work

Department of Media and Communication

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

Abstract

The stability of non-diagonalizable networks of dynamical systems are investigated in detail based on eigenvalue analysis. Pinning control is suggested to stabilize the synchronization state of the whole coupled network. The complicated coupled problem is reduced to two independent problems: clarifying the stable region of the modified system and specifying the eigenvalue distribution of the coupling and control matrix. The dependence of the stability on both pinning density and pinning strength is studied. © 2009 ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering.

Original language	English
Title of host publication	Complex sciences
Subtitle of host publication	first international conference, Complex 2009, Shanghai, China, February 23-25, 2009 : revised papers
Editors	Jie Zhou
Place of Publication	Berlin; New York
Publisher	Springer
Pages	980-990
Volume	4 LNICST
ISBN (Print)	3642024661, 9783642024665, 3642024696, 9783642024658
DOIs	https://doi.org/10.1007/978-3-642-02466-5_98
Publication status	Published - Feb 2009
Event	1st International Conference on Complex Sciences: Theory and Applications, Complex 2009 - Shanghai, China Duration: 23 Feb 2009 → 25 Feb 2009

Publication series

Name	Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering
Volume	4 LNICST
ISSN (Print)	1867-8211

Conference

Conference	1st International Conference on Complex Sciences: Theory and Applications, Complex 2009
Place	China
City	Shanghai
Period	23/02/09 → 25/02/09

Research Keywords

Eigenvalue analysis
Non-diagonalizable network
Pinning control
Stability

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Xiang, L., Chen, Z., & Zhu, J. J. H. (2009). Stability of non-diagonalizable networks: Eigenvalue analysis. In J. Zhou (Ed.), Complex sciences: first international conference, Complex 2009, Shanghai, China, February 23-25, 2009 : revised papers (Vol. 4 LNICST, pp. 980-990). (Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering; Vol. 4 LNICST). Springer . https://doi.org/10.1007/978-3-642-02466-5_98

Xiang, Linying ; Chen, Zengqiang ; Zhu, Jonathan J.H. / Stability of non-diagonalizable networks : Eigenvalue analysis. Complex sciences: first international conference, Complex 2009, Shanghai, China, February 23-25, 2009 : revised papers. editor / Jie Zhou. Vol. 4 LNICST Berlin; New York : Springer , 2009. pp. 980-990 (Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering).

@inproceedings{96b82159c8df4f0ba99afa2453860147,

title = "Stability of non-diagonalizable networks: Eigenvalue analysis",

abstract = "The stability of non-diagonalizable networks of dynamical systems are investigated in detail based on eigenvalue analysis. Pinning control is suggested to stabilize the synchronization state of the whole coupled network. The complicated coupled problem is reduced to two independent problems: clarifying the stable region of the modified system and specifying the eigenvalue distribution of the coupling and control matrix. The dependence of the stability on both pinning density and pinning strength is studied. {\textcopyright} 2009 ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering.",

keywords = "Eigenvalue analysis, Non-diagonalizable network, Pinning control, Stability",

author = "Linying Xiang and Zengqiang Chen and Zhu, \{Jonathan J.H.\}",

year = "2009",

month = feb,

doi = "10.1007/978-3-642-02466-5\_98",

language = "English",

isbn = "3642024661",

volume = "4 LNICST",

series = "Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering",

publisher = "Springer ",

pages = "980--990",

editor = "Jie Zhou",

booktitle = "Complex sciences",

note = "1st International Conference on Complex Sciences: Theory and Applications, Complex 2009 ; Conference date: 23-02-2009 Through 25-02-2009",

}

Xiang, L, Chen, Z & Zhu, JJH 2009, Stability of non-diagonalizable networks: Eigenvalue analysis. in J Zhou (ed.), Complex sciences: first international conference, Complex 2009, Shanghai, China, February 23-25, 2009 : revised papers. vol. 4 LNICST, Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering, vol. 4 LNICST, Springer , Berlin; New York, pp. 980-990, 1st International Conference on Complex Sciences: Theory and Applications, Complex 2009, Shanghai, China, 23/02/09. https://doi.org/10.1007/978-3-642-02466-5_98

Stability of non-diagonalizable networks: Eigenvalue analysis. / Xiang, Linying; Chen, Zengqiang; Zhu, Jonathan J.H.
Complex sciences: first international conference, Complex 2009, Shanghai, China, February 23-25, 2009 : revised papers. ed. / Jie Zhou. Vol. 4 LNICST Berlin; New York: Springer , 2009. p. 980-990 (Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering; Vol. 4 LNICST).

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

TY - GEN

T1 - Stability of non-diagonalizable networks

T2 - 1st International Conference on Complex Sciences: Theory and Applications, Complex 2009

AU - Xiang, Linying

AU - Chen, Zengqiang

AU - Zhu, Jonathan J.H.

PY - 2009/2

Y1 - 2009/2

N2 - The stability of non-diagonalizable networks of dynamical systems are investigated in detail based on eigenvalue analysis. Pinning control is suggested to stabilize the synchronization state of the whole coupled network. The complicated coupled problem is reduced to two independent problems: clarifying the stable region of the modified system and specifying the eigenvalue distribution of the coupling and control matrix. The dependence of the stability on both pinning density and pinning strength is studied. © 2009 ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering.

AB - The stability of non-diagonalizable networks of dynamical systems are investigated in detail based on eigenvalue analysis. Pinning control is suggested to stabilize the synchronization state of the whole coupled network. The complicated coupled problem is reduced to two independent problems: clarifying the stable region of the modified system and specifying the eigenvalue distribution of the coupling and control matrix. The dependence of the stability on both pinning density and pinning strength is studied. © 2009 ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering.

KW - Eigenvalue analysis

KW - Non-diagonalizable network

KW - Pinning control

KW - Stability

UR - https://www.scopus.com/pages/publications/84885885816

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84885885816&origin=recordpage

U2 - 10.1007/978-3-642-02466-5_98

DO - 10.1007/978-3-642-02466-5_98

M3 - RGC 32 - Refereed conference paper (with host publication)

SN - 3642024661

SN - 9783642024665

SN - 3642024696

SN - 9783642024658

VL - 4 LNICST

T3 - Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering

SP - 980

EP - 990

BT - Complex sciences

A2 - Zhou, Jie

PB - Springer

CY - Berlin; New York

Y2 - 23 February 2009 through 25 February 2009

ER -

Xiang L, Chen Z, Zhu JJH. Stability of non-diagonalizable networks: Eigenvalue analysis. In Zhou J, editor, Complex sciences: first international conference, Complex 2009, Shanghai, China, February 23-25, 2009 : revised papers. Vol. 4 LNICST. Berlin; New York: Springer . 2009. p. 980-990. (Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering). doi: 10.1007/978-3-642-02466-5_98

Stability of non-diagonalizable networks: Eigenvalue analysis

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