Lag synchronization of uncertain complex dynamical networks with derivative coupling

Volume 12, Issue 4, pp 252--261 http://dx.doi.org/10.22436/jnsa.012.04.06

Publication Date: December 07, 2018 Submission Date: July 22, 2018 Revision Date: October 05, 2018 Accteptance Date: November 15, 2018

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Authors

Ghada Al-mahbashi - School of mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM, Selangor Darul Ehsan, Malaysia. M. S. M. Noorani - School of mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM, Selangor Darul Ehsan, Malaysia.

Abstract

In this study, uncertain complex dynamical network model with time varying coupling delay and derivative coupling delay is considered. The lag synchronization between two such uncertain networks with different nodes is investigated. An adaptive control method is designed by using Lyapunov stability theory for achieving the lag synchronization and some corollaries are also given. In addition, on the basis of the adaptive update law, unknown parameters of the networks are estimated. The analytical results show that the states of the dynamical network with derivative delay coupling can be asymptotically synchronized under the designed control. The numerical simulation results also demonstrate the validity of the designed method.

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Keywords

• Lag synchronization
• derivative coupling
• complex dynamical networks
• adaptive control

MSC

•  93C40
•  34D06

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