### Finite-time stochastic generalized outer synchronization of time-delayed complex dynamical networks

LI Wang1,2, MA Zhicai2, SHI Hongjun2

1. 1. Basic Department, Jiangsu Xuzhou Medical College, Xuzhou 221008, Jiangsu, China;
2. School of Mathematics, China University of Mining and Technology, Xuzhou 221008, Jiangsu, China
• Received:2016-08-04 Online:2017-06-20 Published:2016-08-04

Abstract: Based on the finite-time control technology and the open-loop control method, the generalized outer synchronization between two complex dynamical networks with time delay and noise perturbation was investigated. A new finite-time controller was designed and the sufficient condition for the finite-time stochastic generalized outer synchronization was obtained based on the finite-time stability theory of stochastic differential equations. The results showed that the synchronization scheme was robust to the noise perturbation. The theoretical results showed that the synchronization time depended on the control strength. Under the same conditions, the synchronization time decreased with the increasing of the control strength. In the numerical examples, the R(¨overo)ssler-like system and Hindmarsh-Rose system were chosen as the node dynamics of the drive and response networks, respectively. The time evolution trajectories of synchronization error and total synchronization error were given. The effectiveness and feasibility of the theoretical result was confirmed by the numerical results.

CLC Number:

• TP13
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