Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 43, Issue 49, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/43/49/495101
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Funding
- National Basic Research Program of China (973 Program) [2007CB310704]
- National Natural Science Foundation of China [90812001, 60821001]
- Foundation for the Author of National Excellent Doctoral Dissertation of PR China (FANEDD) [200951]
- Ministry of Education of China [NCET-10-0239]
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Over the past decade, complex dynamical network synchronization has attracted more and more attention and important developments have been made. In this paper, we explore the scheme of globally exponentially asymptotical synchronization in complex dynamical networks with time delay. Based on Lyapunov stability theory and through defining the error function between adjacent nodes, four novel adaptive controllers are designed under four situations where the Lipschitz constants of the state function in nodes are known or unknown and the network structure is certain or uncertain, respectively. These controllers could not only globally asymptotically synchronize all nodes in networks, but also ensure that the error functions do not exceed the pre-scheduled exponential function. Finally, simulations of the synchronization among the chaotic system in the small-world and scale-free network structures are presented, which prove the effectiveness and feasibility of our controllers.
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