Synchronization of networked harmonic oscillators subject to Markovian jumping coupling strengths

To explore the effect the switching coupling strengths on synchronization of complex dynamical networks, both an impulsive coupling protocol and a piecewise constant coupling protocol are designed by using periodic sampling velocity data for a group of harmonic oscillators. Moreover, the convergence...

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Published inNonlinear dynamics Vol. 91; no. 4; pp. 2607 - 2619
Main Authors Wang, Jingyi, Xu, Chen, Feng, Jianwen, Zhao, Yi
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.03.2018
Springer Nature B.V
Subjects
Automotive Engineering
Classical Mechanics
Control
Coupling
Dynamical Systems
Engineering
Harmonic oscillators
Markov processes
Mechanical Engineering
Original Paper
Switching theory
Synchronism
Vibration
Networked harmonic oscillators
Markovian jumping
Almost sure exponential synchronization
Coupling strengths
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Summary:To explore the effect the switching coupling strengths on synchronization of complex dynamical networks, both an impulsive coupling protocol and a piecewise constant coupling protocol are designed by using periodic sampling velocity data for a group of harmonic oscillators. Moreover, the convergence of these protocols with switching coupling strengths is discussed and some sufficient conditions are established under which the networked harmonic oscillators could achieve collective oscillatory behavior in almost sure sense. It is shown that the almost sure exponential synchronization can be reached even when the coupling strength is switched between enabling and not enabling to achieve synchronization. Finally, some numerical examples are given to illustrate the effectiveness of the theoretical results.
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ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-017-4034-8