Drive network to a desired orbit by pinning control

Quanjun Wu; Hua Zhang

Kybernetika (2015)

  • Volume: 51, Issue: 1, page 150-172
  • ISSN: 0023-5954

Abstract

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The primary objective of the present paper is to develop an approach for analyzing pinning synchronization stability in a complex delayed dynamical network with directed coupling. Some simple yet generic criteria for pinning such coupled network are derived analytically. Compared with some existing works, the primary contribution is that the synchronization manifold could be chosen as a weighted average of all the nodes states in the network for the sake of practical control tactics, which displays the different influences and contributions of the various nodes in synchronization seeking processes of the dynamical network. Furthermore, it is shown that in order to drive a complex network to a desired synchronization state, the coupling strength should vary according to the controller. In addition, the theoretical results about the time-invariant network is extended to the time-varying network, and the result on synchronization problem can also be extended to the consensus problem of networked multi-agent systems. Subsequently, the theoretic results are illustrated by a typical scale-free (SF) neuronal network. Numerical simulations with three kinds of the homogenous solutions, including an equilibrium point, a periodic orbit, and a chaotic attractor, are finally given to demonstrate the effectiveness of the proposed control methodology.

How to cite

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Wu, Quanjun, and Zhang, Hua. "Drive network to a desired orbit by pinning control." Kybernetika 51.1 (2015): 150-172. <http://eudml.org/doc/270033>.

@article{Wu2015,
abstract = {The primary objective of the present paper is to develop an approach for analyzing pinning synchronization stability in a complex delayed dynamical network with directed coupling. Some simple yet generic criteria for pinning such coupled network are derived analytically. Compared with some existing works, the primary contribution is that the synchronization manifold could be chosen as a weighted average of all the nodes states in the network for the sake of practical control tactics, which displays the different influences and contributions of the various nodes in synchronization seeking processes of the dynamical network. Furthermore, it is shown that in order to drive a complex network to a desired synchronization state, the coupling strength should vary according to the controller. In addition, the theoretical results about the time-invariant network is extended to the time-varying network, and the result on synchronization problem can also be extended to the consensus problem of networked multi-agent systems. Subsequently, the theoretic results are illustrated by a typical scale-free (SF) neuronal network. Numerical simulations with three kinds of the homogenous solutions, including an equilibrium point, a periodic orbit, and a chaotic attractor, are finally given to demonstrate the effectiveness of the proposed control methodology.},
author = {Wu, Quanjun, Zhang, Hua},
journal = {Kybernetika},
keywords = {complex dynamical network; pinning control; directed coupling; time delay; DCN oscillator; complex dynamical network; pinning control; directed coupling; time delay; DCN oscillator},
language = {eng},
number = {1},
pages = {150-172},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Drive network to a desired orbit by pinning control},
url = {http://eudml.org/doc/270033},
volume = {51},
year = {2015},
}

TY - JOUR
AU - Wu, Quanjun
AU - Zhang, Hua
TI - Drive network to a desired orbit by pinning control
JO - Kybernetika
PY - 2015
PB - Institute of Information Theory and Automation AS CR
VL - 51
IS - 1
SP - 150
EP - 172
AB - The primary objective of the present paper is to develop an approach for analyzing pinning synchronization stability in a complex delayed dynamical network with directed coupling. Some simple yet generic criteria for pinning such coupled network are derived analytically. Compared with some existing works, the primary contribution is that the synchronization manifold could be chosen as a weighted average of all the nodes states in the network for the sake of practical control tactics, which displays the different influences and contributions of the various nodes in synchronization seeking processes of the dynamical network. Furthermore, it is shown that in order to drive a complex network to a desired synchronization state, the coupling strength should vary according to the controller. In addition, the theoretical results about the time-invariant network is extended to the time-varying network, and the result on synchronization problem can also be extended to the consensus problem of networked multi-agent systems. Subsequently, the theoretic results are illustrated by a typical scale-free (SF) neuronal network. Numerical simulations with three kinds of the homogenous solutions, including an equilibrium point, a periodic orbit, and a chaotic attractor, are finally given to demonstrate the effectiveness of the proposed control methodology.
LA - eng
KW - complex dynamical network; pinning control; directed coupling; time delay; DCN oscillator; complex dynamical network; pinning control; directed coupling; time delay; DCN oscillator
UR - http://eudml.org/doc/270033
ER -

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