Pinning a complex dynamical network to its equilibrium

It is now known that the complexity of network topology has a great impact on the stabilization of complex dynamical networks. In this work, we study the control of random networks and scale-free networks. Conditions are investigated for globally or locally stabilizing such networks. Our strategy is...

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Bibliographic Details
Published in:IEEE transactions on circuits and systems. I, Regular papers Vol. 51; no. 10; pp. 2074 - 2087
Main Authors: Li, Xiang, Wang, Xiaofan, Chen, Guanrong
Format: Journal Article
Language:English
Published: New York IEEE 01.10.2004
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Circuits
Complex networks
Dynamical systems
Dynamics
Feedback control
Internet
IP networks
Lattices
Mathematical analysis
Microscopy
Network topology
Networks
Pinning
Robust stability
Social network services
Stabilization
Strategy
Web sites
ISSN:1549-8328, 1558-0806
Online Access:Get full text
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Summary:It is now known that the complexity of network topology has a great impact on the stabilization of complex dynamical networks. In this work, we study the control of random networks and scale-free networks. Conditions are investigated for globally or locally stabilizing such networks. Our strategy is to apply local feedback control to a small fraction of network nodes. We propose the concept of virtual control for microscopic dynamics throughout the process with different pinning schemes for both random networks and scale-free networks. We explain the main reason why significantly less local controllers are required by specifically pinning the most highly connected nodes in a scale-free network than those required by the randomly pinning scheme, and why there is no significant difference between specifically and randomly pinning schemes for controlling random dynamical networks. We also study the synchronization phenomenon of controlled dynamical networks in the stabilization process, both analytically and numerically.
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ISSN:1549-8328
1558-0806
DOI:10.1109/TCSI.2004.835655