# American Institute of Mathematical Sciences

• Previous Article
Pullback attractors for bi-spatial continuous random dynamical systems and application to stochastic fractional power dissipative equation on an unbounded domain
• DCDS-B Home
• This Issue
• Next Article
Global existence and boundedness of solution of a parabolic-parabolic-ODE chemotaxis-haptotaxis model with (generalized) logistic source
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
##### References:

show all references

##### References:
 [1] Zhengyan Lin, Li-Xin Zhang. Convergence to a self-normalized G-Brownian motion. Probability, Uncertainty and Quantitative Risk, 2017, 2 (0) : 4-. doi: 10.1186/s41546-017-0013-8 [2] Francesca Biagini, Thilo Meyer-Brandis, Bernt Øksendal, Krzysztof Paczka. Optimal control with delayed information flow of systems driven by G-Brownian motion. Probability, Uncertainty and Quantitative Risk, 2018, 3 (0) : 8-. doi: 10.1186/s41546-018-0033-z [3] Yong Ren, Xuejuan Jia, Lanying Hu. Exponential stability of solutions to impulsive stochastic differential equations driven by $G$-Brownian motion. Discrete & Continuous Dynamical Systems - B, 2015, 20 (7) : 2157-2169. doi: 10.3934/dcdsb.2015.20.2157 [4] Defei Zhang, Ping He. Functional solution about stochastic differential equation driven by $G$-Brownian motion. Discrete & Continuous Dynamical Systems - B, 2015, 20 (1) : 281-293. doi: 10.3934/dcdsb.2015.20.281 [5] Yong Ren, Wensheng Yin, Dongjin Zhu. Exponential stability of SDEs driven by $G$-Brownian motion with delayed impulsive effects: average impulsive interval approach. Discrete & Continuous Dynamical Systems - B, 2018, 23 (8) : 3347-3360. doi: 10.3934/dcdsb.2018248 [6] Pengfei Wang, Mengyi Zhang, Huan Su. Input-to-state stability of infinite-dimensional stochastic nonlinear systems. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021066 [7] Ruofeng Rao, Shouming Zhong. Input-to-state stability and no-inputs stabilization of delayed feedback chaotic financial system involved in open and closed economy. Discrete & Continuous Dynamical Systems - S, 2021, 14 (4) : 1375-1393. doi: 10.3934/dcdss.2020280 [8] Yong Ren, Wensheng Yin. Quasi sure exponential stabilization of nonlinear systems via intermittent $G$-Brownian motion. Discrete & Continuous Dynamical Systems - B, 2019, 24 (11) : 5871-5883. doi: 10.3934/dcdsb.2019110 [9] Guolian Wang, Boling Guo. Stochastic Korteweg-de Vries equation driven by fractional Brownian motion. Discrete & Continuous Dynamical Systems, 2015, 35 (11) : 5255-5272. doi: 10.3934/dcds.2015.35.5255 [10] Yong Xu, Rong Guo, Di Liu, Huiqing Zhang, Jinqiao Duan. Stochastic averaging principle for dynamical systems with fractional Brownian motion. Discrete & Continuous Dynamical Systems - B, 2014, 19 (4) : 1197-1212. doi: 10.3934/dcdsb.2014.19.1197 [11] Yong Xu, Bin Pei, Rong Guo. Stochastic averaging for slow-fast dynamical systems with fractional Brownian motion. Discrete & Continuous Dynamical Systems - B, 2015, 20 (7) : 2257-2267. doi: 10.3934/dcdsb.2015.20.2257 [12] Andrii Mironchenko, Hiroshi Ito. Characterizations of integral input-to-state stability for bilinear systems in infinite dimensions. Mathematical Control & Related Fields, 2016, 6 (3) : 447-466. doi: 10.3934/mcrf.2016011 [13] María J. Garrido–Atienza, Kening Lu, Björn Schmalfuss. Random dynamical systems for stochastic partial differential equations driven by a fractional Brownian motion. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 473-493. doi: 10.3934/dcdsb.2010.14.473 [14] Jin Li, Jianhua Huang. Dynamics of a 2D Stochastic non-Newtonian fluid driven by fractional Brownian motion. Discrete & Continuous Dynamical Systems - B, 2012, 17 (7) : 2483-2508. doi: 10.3934/dcdsb.2012.17.2483 [15] Bin Pei, Yong Xu, Yuzhen Bai. Convergence of p-th mean in an averaging principle for stochastic partial differential equations driven by fractional Brownian motion. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 1141-1158. doi: 10.3934/dcdsb.2019213 [16] Tadahisa Funaki, Yueyuan Gao, Danielle Hilhorst. Convergence of a finite volume scheme for a stochastic conservation law involving a $Q$-brownian motion. Discrete & Continuous Dynamical Systems - B, 2018, 23 (4) : 1459-1502. doi: 10.3934/dcdsb.2018159 [17] Shaokuan Chen, Shanjian Tang. Semi-linear backward stochastic integral partial differential equations driven by a Brownian motion and a Poisson point process. Mathematical Control & Related Fields, 2015, 5 (3) : 401-434. doi: 10.3934/mcrf.2015.5.401 [18] Litan Yan, Xiuwei Yin. Optimal error estimates for fractional stochastic partial differential equation with fractional Brownian motion. Discrete & Continuous Dynamical Systems - B, 2019, 24 (2) : 615-635. doi: 10.3934/dcdsb.2018199 [19] Ahmed Boudaoui, Tomás Caraballo, Abdelghani Ouahab. Stochastic differential equations with non-instantaneous impulses driven by a fractional Brownian motion. Discrete & Continuous Dynamical Systems - B, 2017, 22 (7) : 2521-2541. doi: 10.3934/dcdsb.2017084 [20] Henryk Leszczyński, Monika Wrzosek. Newton's method for nonlinear stochastic wave equations driven by one-dimensional Brownian motion. Mathematical Biosciences & Engineering, 2017, 14 (1) : 237-248. doi: 10.3934/mbe.2017015

2019 Impact Factor: 1.27