Global exponential periodicity and stability of memristor-based complex-valued delayed neural networks

ABSTRACT

This paper concentrates on the dynamical behaviours of memristor-based complex-valued delayed neural networks. By constructing the appropriate Lyapunov functional and utilising some inequality techniques, sufficient conditions are proposed to guarantee the existence and global exponential stability of the periodic solution of the considered system. The proposed results not only generalise some previously related literatures, but also are easy to be checked with the parameters of system itself. In addition, the theoretical results of this paper may be helpful in qualitative analysis for complex-valued nonlinear delayed systems. A numerical example is given to demonstrate the effectiveness of the proposed results.

KEYWORDS:

• Periodic solution
• stability
• complex-valued neural networks
• time-varying systems
• nonlinear systems

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Fundamental Research Funds for the Central Universities [grant number 2014XT02].

Notes on contributors

Dan Liu

Dan Liu was born in 1990. He received the B.S. degree in Applied Mathematics in 2015 from Northwest University for Nationalities, Lanzhou, China. He is currently pursuing the M.S degree with the Operational Research and Cybernetics, China University of Mining and Technology, Xuzhou, China. His current research interests include the areas of neural networks and stochastic control.

Song Zhu

Song Zhu was born in 1982. He received the B.S. degree in Mathematics in 2004 from Jiangsu Normal University, Xuzhou, China, the M.S. degree in Probability and Mathematical Statistics in 2007, Ph.D. degree in System Engineering in 2010, from Huazhong University of Science and Technology, Wuhan, China, respectively. He is currently associate Professor with the College of Sciences, China University of Mining and Technology, Xuzhou, China. He has authored over 30 research papers. His research is concerned with neural networks and stochastic control.

Er Ye

Er Yewas born in 1993. She received the B.S. degree in Applied Mathematics in 2015 from Northwest University for Nationalities, Lanzhou, China. She is currently pursuing the M.S degree with the Fundamental Mathematics, Southeast University, Nanjing, China. Her current research interests include the areas of generalied inverse, complex-valued system.