Journal
APPLIED MATHEMATICAL MODELLING
Volume 39, Issue 18, Pages 5636-5649Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2015.01.027
Keywords
Complex networks; Markov chain; Ergodic theory; Matrix measure; Synchronization
Funding
- National Natural Science Foundation of China [61272530]
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This paper devotes to almost sure synchronization and almost sure quasi-synchronization of complex networks with Markov switching. Some sufficient conditions are derived in terms of the ergodic theory of continuous time Markov chain and the matrix measure approach, which can guarantee that the dynamical networks almost surely synchronize or quasi-synchronize to a given manifold. According to the property of Markov chain and the exponential distribution of switching time sequence, we also estimate the probability distribution of the quasi-synchronization error for a two-state Markov chain and then generalize them to a finite state space Markov chain. Meanwhile, some examples with numerical simulations are given to show that the Markov chain plays an important role in synchronization of networks. (C) 2015 Elsevier Inc. All rights reserved.
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