Cluster synchronization in fractional-order network with nondelay and delay coupling

Yi Wang () and Zhaoyan Wu
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Yi Wang: School of Mathematics and Statistics, Jiangxi Normal University, Nanchang, Jiangxi Province 330022, P. R. China
Zhaoyan Wu: School of Mathematics and Statistics, Jiangxi Normal University, Nanchang, Jiangxi Province 330022, P. R. China

International Journal of Modern Physics C (IJMPC), 2022, vol. 33, issue 01, 1-15

Abstract: In this paper, cluster synchronization for fractional-order complex network with nondelay and delay coupling is investigated. Based on the stability theory of fractional-order systems and the properties of fractional derivative, both static and adaptive control schemes are adopted to design effective controllers. Sufficient condition for achieving cluster synchronization about static controllers is provided. From the condition, the needed feedback gains can be estimated by simple calculations. Further, adaptive control scheme is introduced to design unified controllers. Noticeably, in the adaptive controllers, the feedback gains need not be calculated in advance and can adjust themselves to the needed values according to updating laws. Finally, numerical simulations are given to demonstrate the correctness of the obtained results.

Keywords: Cluster synchronization; fractional-order network; adaptive control; time delay (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0129183122500061

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