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Stochastic mean square exponential synchronisation of time-varying complex dynamical networks via pinning control |
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| Authors: | Xin Wang Xinzhi Liu Kun She Shouming Zhong Kaibo Shi |
| Affiliation: | 1. School of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu, P.R. China;2. Department of Applied Mathematics, University of Waterloo, Waterloo, Canada;3. Department of Applied Mathematics, University of Waterloo, Waterloo, Canada;4. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, P.R. China;5. School of Information Science and Engineering, Chengdu University, Chengdu, P.R. China |
| Abstract: | This paper investigates the problem of stochastic mean square exponential synchronisation of complex dynamical networks with time-varying delay via pinning control. By applying the Lyapunov method and stochastic analysis, criteria on mean square exponential synchronisation are established under linear feedback pinning control and adaptive feedback pinning control, which depend on the time-varying delay and stochastic perturbation. These results complement and improve the previously known results. Two numerical examples are given to illustrate the effectiveness and correctness of the derived theoretical results. |
| Keywords: | Exponential synchronisation stochastic dynamical networks pinning control time-varying delay |