Finite-time synchronisation of delayed fractional-order coupled neural networks

Abstract

This paper considers the global synchronisation and finite-time synchronisation for a class of delayed fractional-order complex neural networks (DFOCNNs). Based on the properties of fractional-order calculus and the Razumikhin-type Lyapunov theorem of a fractional-order system, two new lemmas are proved. These lemmas are employed to formulate a couple of novel criteria for both finite-time synchronisation and global synchronisation of DFOCNNs. Moreover, the upper bound of the setting time for synchronisation is given. Three examples are provided to verify the effectiveness of the obtained results.

Keywords:

• Finite-time synchronisation
• fractional order
• Razumikhin-type theorem
• global synchronisation

Acknowledgments

The authors would like to thank the editor and anonymous reviewers.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The authors confirm that the data supporting the findings of this study are available within the article.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [61271355, 61773404].

Notes on contributors

Shuailei Zhang

Shuailei Zhang was born in 1997. He received the B.S. and M.S. degrees from Central South University, Changsha, China in 2018, and 2021. He is currently pursuing the Ph.D. degree in Operational Research and Cybernetics, Central South University. His current research interest is in the theory of stability for fractional-order system.

Xinge Liu

Xinge Liu was born in 1969, received the B.S. and M.S. degrees from Hunan Normal University, Changsha, China and the Ph.D. degree from Central South University, Changsha, China, all in mathematics, in 1991, 1994, and 2001, respectively. In May 1994, he joined the School of Mathematics and Statistics, Central South University, where he is currently a professor. From 2002 to 2004, he was a postdoctor of Automatic Control Engineering, Central South University. From October 2004 to September 2006, he was a postdoctor and visiting scholar in the School of Computer Science, Cardiff University, Cardiff, U.K. In 2008 he was approved to be a doctorial advisor. His research interests include neural networks, stability theory, functional differential (difference) equations, inequality theory, and harmonic analysis.

Xuemei Li

Xuemei Li was born in 1992. She received her B.S. in Applied Mathematics from Hunan City University in Yiyang, China in 2014, and her M.S. in Applied Mathematics from Guangxi University for Nationalities in Nanning, China in 2017. She is now working on her Ph.D. in Applied Mathematics at Central South University. Her current research interests include fractional system stability and control theory.