Pinning a complex dynamical network to its equilibrium
Xiang Li
Xiaofan Wang
Guanrong Chen
Dept. of Autom., Shanghai Jiaotong Univ., China;
This paper appears in: Circuits and Systems I: Regular Papers, IEEE Transactions on
Publication Date: Oct. 2004
Volume: 51,
Issue: 10
On page(s): 2074- 2087
ISSN: 1549-8328
INSPEC Accession Number: 8157539
Digital Object Identifier: 10.1109/TCSI.2004.835655
Current Version Published: 2004-10-18
Abstract
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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