Neural Networks 53 (2014) 8–14 Contents lists available at ScienceDirect Neural Networks journal homepage: www.elsevier.com/locate/neunet Synchronization control of memristor-based recurrent neural networks with perturbations Weiping Wang a , Lixiang Li b,∗ , Haipeng Peng b,c , Jinghua Xiao a , Yixian Yang b a School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China b Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China c Zhejiang Provincial Key Lab of Data Storage and Transmission Technology, Hangzhou Dianzi University, Hangzhou 310018, Zhejiang, China article info Article history: Received 21 June 2013 Received in revised form 12 January 2014 Accepted 21 January 2014 Keywords: Memristor-based recurrent neural networks Synchronization control Impulsive perturbation Boundary perturbation abstract In this paper, the synchronization control of memristor-based recurrent neural networks with impulsive perturbations or boundary perturbations is studied. We find that the memristive connection weights have a certain relationship with the stability of the system. Some criteria are obtained to guarantee that memristive neural networks have strong noise tolerance capability. Two kinds of controllers are designed so that the memristive neural networks with perturbations can converge to the equilibrium points, which evoke human’s memory patterns. The analysis in this paper employs the differential inclusions theory and the Lyapunov functional method. Numerical examples are given to show the effectiveness of our results. Crown Copyright © 2014 Published by Elsevier Ltd. All rights reserved. 1. Introduction The memristor is considered to be the fourth passive circuit ele- ment, originally predicted by Chua (1971) in 1971. The first practi- cal memristor device was invented by scientists in 2008 (Strukov, Snider, Stewart, & Williams, 2008). The memristor retains its most recent value when the voltage is turned off, so it re-expresses that value the next time it is turned on. That feature makes them use- ful as energy-saving devices that can compete with flash memory and other static memory devices. Some classes of memristors also have non-linear response characteristics which makes them dou- bly suitable as artificial neurons. More and more researchers have been focusing on the memristor because of its potential applica- tions in next generation computers and powerful brain-link ‘‘neu- ral’’ computers. Over recent decades, in order to process information intelli- gently, people set up artificial neural networks to simulate the function of human brain. Traditional hardware implementations of artificial neural network have used fixed value resistors be- tween neural processing units, which are supposed to represent the strength of synaptic connections between neurons in biology. The strength of synapses is variable while the resistance is invari- able. In order to simulate the artificial neural network of human ∗ Corresponding author. Tel.: +86 010 62282264. E-mail address: li_lixiang2006@163.com (L. Li). brain better, the resistor is replaced by the memristor which even- tually may be used in hardware and software of artificial neu- ral networks. Recently, Wu, Wen, and Zeng (2012), Wu and Zeng (2012), Wu and Zhang (2013), Wu, Zhang, and Zeng (2011), and Zhang, Shen, and Wang (2013) have concentrated on the dynamical nature of the memristor-based neural networks in order to achieve its successful applications in many different fields, such as pattern recognition, associative memories and learning, in a way that mim- ics the human brain. In the real world, random uncertainties (e.g. instantaneous in- terference on neural systems) make the neural networks change their states suddenly, which lead to the impulsive effect. Li and Chen (2009) study the stability properties for Hopfield neural net- works with delays and impulsive perturbations. Besides impul- sive perturbations, Gu (2009), Li and Cao (2008), Li, Ding, and Zhu (2010), Zhou, Wang, and Mou (2012), and Zhu, Yang, and Wang (2010) have studied stochastic perturbations on neural networks, since a real system is usually affected by external perturbations which in many cases are of great uncertainties and such pertur- bations may be treated as fluctuations from the release of neuro- transmitters and other probabilistic causes. Furthermore, from the logical analysis of mathematical reason- ing, many people have studied the noise tolerance on artificial neural networks, and the obtained results have a certain robust- ness. Then we want to know, do the memristive neural networks also have strong noise tolerance capability? Knowing that associa- tive memory can be obtained from artificial neural networks, the 0893-6080/$ – see front matter Crown Copyright © 2014 Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.neunet.2014.01.010