Delay-dependent cluster synchronization of time-varying complex dynamical networks with noise via delayed pinning impulsive control |
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| Authors: | Guang Ling Xinzhi Liu Ming-Feng Ge Yonghong Wu |
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| Institution: | 1. School of Science, Wuhan University of Technology, Wuhan 430070, China;2. Department of Applied Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada;3. School of Mechanical Engineering and Electronic Information, China University of Geosciences, Wuhan 430074, China;1. School of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan 610031, PR China;2. School of Mathematics Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, PR China;1. School of Computer Science and Software Engineering, Tianjin Polytechnic University, Tianjin 300387, China;2. Tianjin Key Laboratory of Optoelectronic Detection Technology and System, Tianjin Polytechnic University, Tianjin 300387, China;3. School of Mechanical Engineering, Tianjin Polytechnic University, Tianjin 300387, China;1. Department of Mathematics, Chongqing Normal University, Chongqing 401331, China;2. College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China |
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| Abstract: | This paper investigates the problem of cluster synchronization of complex dynamical networks with noise and time-varying delays by using a delayed pinning impulsive control scheme. Different from the traditional impulsive control schemes without the effects of input delays, it designs a pinning impulsive control scheme to successfully address the aforementioned problem subject to impulsive input delays. By employing a time-dependent Lyapunov function and the mathematical induction, some novel criteria are established to guarantee the cluster synchronization of the noisy complex networks, revealing the closed relationship between the synchronization performance and the related factors, including the impulsive input delays, the number of the pinned nodes, the frequency and strength of the impulsive control, and the noisy perturbations. Some numerical examples and computer simulations are presented to illustrate the effectiveness of the theoretical results. |
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