Pinning control of complex dynamical networks with general topology

Recently, the researches on pinning control of complex dynamical networks have mainly focused on such networks with very specific coupling schemes (e.g., symmetric coupling, uniform coupling and linear coupling). However, most real networks often consist of local units, which interact with each othe...

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Bibliographic Details
Published in:Physica A 2007-06, Vol.379 (1), p.298-306
Main Authors: Xiang, L.Y., Liu, Z.X., Chen, Z.Q., Chen, F., Yuan, Z.Z.
Format: Article
Language:English
Subjects:
Complex dynamical network
Directed graph
Master stability function
Pinning control
Transverse Lyapunov exponents (TLEs)
Weighted networks
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Summary:Recently, the researches on pinning control of complex dynamical networks have mainly focused on such networks with very specific coupling schemes (e.g., symmetric coupling, uniform coupling and linear coupling). However, most real networks often consist of local units, which interact with each other via asymmetric and heterogeneous connections. In this paper, pinning control of a continuous-time complex dynamical network with general coupling topologies is studied. Some generic stability criteria based on master stability function (MSF) are derived for such a general controlled network, which guarantee that the whole network can be pinned to its equilibrium by placing feedback control only on a small fraction of nodes. Then, these results are extended to discrete-time case. Previous results about symmetric, uniform or linear coupled networks in this area are included as special cases of the present work. Numerical simulations of directed networks with weighted coupling pinned by specifically selective pinning scheme are given for illustration and verification.
ISSN:0378-4371
1873-2119
DOI:10.1016/j.physa.2006.12.037