Global exponential anti-synchronization for delayed memristive neural networks via event-triggering method
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ORIGINAL ARTICLE
Global exponential anti-synchronization for delayed memristive neural networks via event-triggering method Xiaoze Ni1 • Yuting Cao2 • Zhenyuan Guo2 • Tingwen Huang3 • Shiping Wen1 Received: 26 October 2019 / Accepted: 24 January 2020 Ó Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract This paper studies the exponential anti-synchronization problem of memristive delayed neural networks under the eventtriggered controller. To reduce the recalculation of the control signals, two event-triggered control strategies including static and dynamic are proposed. A novel Lyapunov function is constructed to analyze the global exponential antisynchronization problem. By analysis, we can choose the suitable parameter of the controller to realize global exponential anti-synchronization with a given convergence rate c without wasting a lot of control resources. Moreover, under eventtriggering conditions given in our theorem, we derive that the Zeno behavior will not happen. Finally, numerical examples are given to validate our theorem. Keywords Memristive neural network Time-varying delay Event-triggered control Global exponential antisynchronization Zeno behavior
1 Introduction Artificial neural networks (ANNs) have been widely studied since the 1980s. Connections between traditional neural network neurons are usually simulated with resistance, which makes their weights fixed [5, 24, 30, 38, 41, 42, 49]. The memristor, which was postulated in 1971 [4], was announced to be built by a research team at Hewlett-Packard Laboratory in 2008 [31]. Since memristor has a characteristic of variable resistance, which is mainly depended on the history of flowing current, a novel network called memristive neural network (MNN) is built by replacing the resistance with the memristor. Some great characteristics of memristor like variable
& Shiping Wen [email protected] 1
School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
2
School of Mathematics and Econometrics, Hunan University, Changsha 410082, China
3
Science Program, Texas A&M University at Qatar, Doha 23874, Qatar
resistance and non-volatility make its performances better than traditional neural network [10, 12, 13, 35, 36, 40, 45]. Researches on the dynamical characteristic analysis of ANN have been paid a great attention due to their successful applications like secure communications [17, 19], natural language processing [44], image processing [7, 8, 16, 26–28, 33, 37, 43, 46, 50, 56] and so on. There are extensive researches on dynamic performance of MNN such as passivity and passification, see [2, 15, 29, 34], stability and stabilization, see [14, 20, 39, 51], dissipativity, see [23] and so on. Synchronization, as one of the essential attributes of two dynamical systems, has been extensively studied. For example, finite-time synchronization has been researched for delayed MNNs in [1], and the global synchronizatio
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