Pinning synchronization of fractional-order memristor-based neural networks with multiple time-varying delays via static or dynamic coupling |
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| Authors: | Jia Jia Zhigang Zeng Fei Wang |
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| Institution: | 1. School of Artificial Intelligence and Automation, the Key Laboratory of Image Processing and Intelligent Control, Huazhong University of Science and Technology, Wuhan 430074, China;2. School of Control Science and Engineering, Shandong University, Jinan 250061, China;3. School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, China;1. Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, China;2. School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, 100081, China;1. School of Mathematics, Southeast University, Nanjing 210096, China;2. College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China;3. Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia;1. Department of Mathematics, Alagappa University, Karaikudi 630004, India;2. Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi 630004, India;3. School of Mathematics, Southeast University, Nanjing 211189, China;4. School of Mathematics and Statistics, Shandong Normal University, Ji’nan 250014, China;5. Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai, Thailand;6. Department of Information Systems, Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah, Saudi Arabia |
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| Abstract: | This paper investigates global asymptotical synchronization between fractional-order memristor-based neural networks (FMNNs) with multiple time-varying delays (MTDs) by pinning control. Two classes of coupling manners, static manner and dynamic manner, are introduced into the pinning controller respectively. For the case of static coupling, to make the controller exclude fraction, 1-norm Lyapunov function and fractional Halanay inequality in MTDs case are utilized for synthesis of controller and convergence analysis of synchronization error. For the case of dynamic coupling, a fractional differential inequality is proved and discussed in an elaborate way, and then global asymptotical synchronization is analyzed by means of Lyapunov-like function and the newly-proved inequality. Lastly, numerical simulations are carried out to show the practicability of the pinning controllers and the feasibility of the obtained synchronization criteria. |
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