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July  2019, 24(7): 3379-3393. doi: 10.3934/dcdsb.2018325

## Weighted exponential stability of stochastic coupled systems on networks with delay driven by $G$-Brownian motion

 1 School of Mathematics and Statistics, Lingnan Normal University, Zhanjiang 524048, China 2 Department of Mathematics, Anhui Normal University, Wuhu 241000, China 3 School of Mathematics, Southeast University, Nanjing 211189, China

* Corresponding author: Yong Ren, Correspondence to Department of Mathematics, Anhui Normal University, Wuhu 241000, China

Received  April 2018 Revised  July 2018 Published  January 2019

Fund Project: This work is supported by the National Natural Science Foundation of China (11871076).

This paper investigates the issue of weighted exponentially input to state stability (EISS, in short) of stochastic coupled systems on networks with time-varying delay driven by $G$-Brownian motion ($G$-SCSND, in short). Combining with inequality technique, $k$th vertex-Lyapunov functions and graph-theory, we establish the weighted EISS for $G$-SCSND. An application to the EISS for a class of stochastic coupled oscillators networks with control inputs driven by $G$-Brownian motion and an example are provided to illustrate the effectiveness of the obtained theory.

Citation: Yong Ren, Huijin Yang, Wensheng Yin. Weighted exponential stability of stochastic coupled systems on networks with delay driven by $G$-Brownian motion. Discrete & Continuous Dynamical Systems - B, 2019, 24 (7) : 3379-3393. doi: 10.3934/dcdsb.2018325
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