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Abstract
This paper is concerned with the issue of mean square cluster synchronisation in complex networks, which consist of non-identical nodes with randomly occurring non-linearities. In order to guarantee synchronisation, distributed controllers depending on the information from the neighbours in the same cluster are applied to each node, meanwhile, the control gains are supposed to be updated according to the given laws. Based on the Lyapunov stability theory, the sufficient synchronisation conditions are derived and proved theoretically. Finally, a numerical example is presented to demonstrate the effectiveness of the results.
Additional information
Notes on contributors
Aihua Hu
Aihua Hu received the BS degree in information and computing science from the Jiangnan University, Wuxi, China, in 2003, and the MS degree and PhD degree in control theory and engineering from the Jiangnan University, Wuxi, China, in 2006 and 2010, respectively. From June 2012 to June 2014, she was a postdoctoral research fellow at the School of Automation, Southeast University, Nanjing, China. Currently, she is an associate professor and graduate student advisor at the Jiangnan University. She is the author or co-author of about 20 journal papers. Her research interests include non-linear systems, stochastic systems, and complex networks.
Jinde Cao
Jinde Cao received the BS degree from Anhui Normal University, Wuhu, China, the MS degree from Yunnan University, Kunming, China, and the PhD degree from Sichuan University, Chengdu, China, all in applied mathematics, in 1986, 1989, and 1998, respectively. From March 1989 to May 2000, he joined the Department of Mathematics, Southeast University, Nanjing, China. From July 2001 to June 2002, he was a postdoctoral research fellow at the Department of Automation and Computer-Aided Engineering, Chinese University of Hong Kong, Hong Kong. In the period from 2006 to 2008, he was a visiting research fellow and a visiting professor at the School of Information System, Computing and Mathematics, Brunel University, UK. Currently, he is a distinguished professor and doctoral advisor at the Southeast University and also distinguished adjunct professor at the King Abdulaziz University, prior to which he was a professor at Yunnan University from 1996 to 2000. He is the author or co-author of 400 journal papers and five edited books. His research interests include non-linear systems, neural networks, complex systems, complex networks, stability theory, and applied mathematics. Dr Cao was an associate editor of the IEEE Transactions on Neural Networksand Journal of the Franklin Institute and Neurocomputing. He is an associate editor of the IEEE Transactions on Cybernetics, Neural Networks, Differential Equations and Dynamical Systems, and Mathematics and Computers in Simulation.
Manfeng Hu
Manfeng Hu received both the BS and MS degrees from Xuzhou Normal University, Xuzhou, China, and the PhD degree from Jiangnan University, Wuxi, China, in 1998, 2001, and 2008, respectively. He was a visiting scholar at the Department of Mathematics, Michigan State University, USA, from June 2008 to June 2009. From April 2011 to July 2013, he was a postdoctoral research fellow at the School of Automation, Southeast University, Nanjing, China. Since July 2008, he has been an associate professor at Jiangnan University. His current research interests include non-linear dynamics, dynamics of complex networks, and system biology.
Liuxiao Guo
Liuxiao Guo received the BS degree and MS degree from Soochow University, Suzhou, China, and the PhD degree from Jiangnan University, Wuxi, China, all in mathematics and applied mathematics, in 1993, 1997, and 2000, respectively. In 2006, she was a visiting scholar in the University of Sydney, Australia. Currently, she is an associate professor and graduate student advisor at the Jiangnan University. She is the author or co-author of about 20 journal papers and one edited book. Her research interests include non-linear systems, complex systems, stability theory, and applied mathematics.