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Periodic Dynamics for Memristor-based Bidirectional Associative Memory Neural Networks with Leakage Delays and Time-varying Delays

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  • Control Theory and Applications
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Abstract

This paper deals with a class of memristor-based bidirectional associative memory (BAM) neural networks with leakage delays and time-varying delays. With the aid of the framework of Filippov solutions, Chain rule and some inequality techniques, a sufficient condition which ensures the boundedness and ultimate boundedness of solutions of memristor-based BAM neural networks with leakage delays and time-varying delays is established. Applying a new approach involving Yoshizawa-like theorem, we prove the existence of periodic solution of the memristor-based BAM neural networks. By using the theory of set-valued maps and functional differential inclusions, Lyapunov functional, a set of sufficient conditions which guarantee the uniqueness and global exponential stability of periodic solution of memristor-based BAM neural networks are derived. An example is given to illustrate the applicability and effectiveness of the theoretical predictions. The results obtained in this paper are completely new and complement the previously known studies of Li et al. [Existence and global exponential stability of periodic solution of memristor-based BAM neural networks with time-varying delays, Neural networks 75 (2016) 97-109.]

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Author information

Authors and Affiliations

  1. Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang, 550004, P. R. China

    Changjin Xu

  2. School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471023, P. R. China

    Peiluan Li

Authors
  1. Changjin Xu
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  2. Peiluan Li
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Correspondence to Changjin Xu.

Additional information

Recommended by Editor Jessie (Ju H.) Park. This journal was supported by the National Natural Science Foundation of China (No.61673008 and No.11261010), the Project of High-level Innovative Talents of Guizhou Province ([2016]5651), the Major Research Project of The Innovation Group of The Education Department of Guizhou Province( [2017]039) and Project of Key Laboratory of Guizhou Province with Financial and Physical Features ([2017]004).

Changjin Xu received the Ph.D. and M.S. degrees in Applied Mathematics from Central South University, China, in 2010, Kunming University of Science and Technology, China, in 2004. He is currently a professor at the Guizhou Key Laboratory of Economics System Simulation at Guizhou University of Finance and Economics. He has published about 100 refereed journal papers. He is a Reviewer of Mathematical Reviews and Zentralblatt MATH. His research interests include stability and bifurcation theory of delayed differential equation.

Peiluan Li received the Ph.D. and M.S. degrees in Applied Mathematics from Central South University, China, in 2010, Wuhan University, China, in 2004. He was a postdoctoral from 2011 to 2013 in Hunan Normal University, China. He is currently an associate professor at the School of Mathematics and Statistics of Henan University of Science and Technology. He has published about 70 refereed journal papers. His research interests include nonlinear systems, functional differential equations, boundary value problems.

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Xu, C., Li, P. Periodic Dynamics for Memristor-based Bidirectional Associative Memory Neural Networks with Leakage Delays and Time-varying Delays. Int. J. Control Autom. Syst. 16, 535–549 (2018). https://doi.org/10.1007/s12555-017-0235-7

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  • DOI: https://doi.org/10.1007/s12555-017-0235-7

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