Pinning-controlled synchronization of complex networks with bounded or unbounded synchronized regions |
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| Authors: | Zou Yan-Li and Chen Guan-Rong |
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| Affiliation: | College of Physics and Electronic Engineering, Guangxi Normal University, Guilin 541004, China; Department of Electronic Engineering, City University of Hong Kong, Hong Kong SAR, China |
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| Abstract: | This paper studies pinning-controlled synchronization of complex
networks with bounded or unbounded synchronized regions. To study a
state-feedback pinning-controlled network with N nodes, it first
converts the controlled network to an extended network of N+1
nodes without controls. It is shown that the controlled
synchronizability of the given network is determined by the real
part of the smallest nonzero eigenvalue of the coupling matrix of
its extended network when the synchronized region is unbounded; but
it is determined by the ratio of the real parts of the largest and
the smallest nonzero eigenvalues of the coupling matrix when the
synchronized region is bounded. Both theoretical analysis and
numerical simulation show that the portion of controlled nodes has
no critical values when the synchronized region is unbounded, but it
has a critical value when the synchronized region is bounded. In the
former case, therefore, it is possible to control the network to
achieve synchronization by pinning only one node. In the latter
case, the network can achieve controlled synchronization only when
the portion of controlled nodes is larger than the critical value. |
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| Keywords: | synchronization pinning
control complex network synchronized region |
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