Synchronisation control for a class of complex-valued fractional-order memristor-based delayed neural networks

Abstract

In this paper, the problem of drive-response synchronisation of complex-valued fractional-order memristor-based delayed neural networks is discussed via linear feedback control method. By separating complex-valued system into two equivalent real-valued systems, and using the comparison theorem, algebraic criteria are given to ascertain the synchronisation of the considered system with single delay. Meanwhile, for the case of model with multiple delays, the corresponding sufficient conditions are also presented. Because complex-valued system can reduce to real-valued ones when the imaginary part is ignored, the proposed results of this paper generalise existing works on relevant real-valued system. Finally, the effectiveness of the obtained theoretical results is testified by two numerical examples.

Keywords:

• Fractional-order system
• complex-valued neural networks
• memristor
• synchronisation
• linear feedback control

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by in part by National Natural Science Foundation of China [grant numbers 61773097, U1813214], the Fundamental Research Funds for the Central Universities [grant number N160402004].

Notes on contributors

Dan Liu

Dan Liu received the B.S. degree in applied mathematics in 2015 from Northwest University for Nationalities, Lanzhou, China, and the M.S. degree in operational research and cybernetics in 2018 from China University of Mining and Technology, Xuzhou, China. He is currently pursuing the Ph.D. degree in control theory and engineering from the Northeastern University, Shenyang, China. His current research interests include the areas of neural networks and complex dynamic networks.

Dan Ye

Dan Ye received the B.S. and M.S. degrees in mathematics and applied mathematics from Northeast Normal University, China in 2001 and 2004, respectively, and the Ph. D. degree in control theory and engineering from the Northeastern University in 2008. She was a lecturer with the Northeastern University from 2008 to 2010. Currently, she is a professor of the College of Information Science and Engineering, Northeastern University, China. Her research interest includes fault-tolerant control, robust control, adaptive control and security of cyber-physical systems.