The stability of memristive multidirectional associative memory neural networks with time-varying delays in the leakage terms via sampled-data control

Weiping Wang; Xin Yu; Xiong Luo; Long Wang; Lixiang Li; Jürgen Kurths; Wenbing Zhao; Jiuhong Xiao

doi:10.1371/journal.pone.0204002

The stability of memristive multidirectional associative memory neural networks with time-varying delays in the leakage terms via sampled-data control

PLoS One. 2018 Sep 24;13(9):e0204002. doi: 10.1371/journal.pone.0204002. eCollection 2018.

Authors

Weiping Wang^{1

2

3}, Xin Yu^{1

2}, Xiong Luo^{1

2}, Long Wang^{1

2}, Lixiang Li⁴, Jürgen Kurths^{3

5}, Wenbing Zhao⁶, Jiuhong Xiao⁷

Affiliations

¹ School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing, China.
² Beijing Key Laboratory of Knowledge Engineering for Materials Science, Beijing, China.
³ Institute of Physics, Humboldt-University, Berlin, Germany.
⁴ Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, China.
⁵ Potsdam Institute for Climate Impact Research, Potsdam, Germany.
⁶ Department of Electrical Engineering and Computer Science, Cleveland State University, Cleveland, Ohio, United States of America.
⁷ School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, China.

Abstract

In this paper, we propose a new model of memristive multidirectional associative memory neural networks, which concludes the time-varying delays in leakage terms via sampled-data control. We use the input delay method to turn the sampling system into a continuous time-delaying system. Then we analyze the exponential stability and asymptotic stability of the equilibrium points for this model. By constructing a suitable Lyapunov function, using the Lyapunov stability theorem and some inequality techniques, some sufficient criteria for ensuring the stability of equilibrium points are obtained. Finally, numerical examples are given to demonstrate the effectiveness of our results.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Association
Brain / physiology
Computer Simulation
Humans
Mathematical Concepts
Memory* / physiology
Models, Neurological
Models, Psychological
Nerve Net / physiology
Neural Networks, Computer*
Systems Theory
Time Factors

Grants and funding

This work was supported by the National Key Research and Development Program of China under Grants 2017YFB0702300, the State Scholarship Fund of China Scholarship Council (CSC), the National Natural Science Foundation of China under Grants 61603032 and 61174103, the Fundamental Research Funds for the Central Universities under Grant 06500025, and the University of Science and Technology Beijing-National Taipei University of Technology Joint Research Program under Grant TW201705.