Estimation of the time cost with pinning control for stochastic complex networks

Jiaqi Chang; Xiangxin Yin; Caoyuan Ma; Donghua Zhao; Yongzheng Sun; Jiaqi Chang; Xiangxin Yin; Caoyuan Ma; Donghua Zhao; Yongzheng Sun

doi:10.3934/era.2022179

Electronic Research Archive

2022, Volume 30, Issue 9: 3509-3526. doi: 10.3934/era.2022179

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Estimation of the time cost with pinning control for stochastic complex networks

1.
School of Mathematical Sciences, China University of Mining and Technology, Xuzhou 221116, China
2.
School of Electrical Engineering, China University of Mining and Technology, Xuzhou 221116, China
3.
School of Mathematical Sciences, Fudan University, Shanghai 200433, China

Academic Editor: Wei Lin

Received: 16 May 2022 Revised: 08 July 2022 Accepted: 18 July 2022 Published: 27 July 2022

In this paper, the finite-time and fixed-time stochastic synchronization of complex networks with pinning control are investigated. Considering the time and energy cost of control, combining the advantages of finite-time control technology and pinning control technology, efficient protocols are proposed. Compared with the existing research, the influence of noise is considered, and sufficient conditions for the network to achieve stochastic synchronization in a finite time are given in this paper. Based on the stability theory of stochastic differential equations, the upper bound of the setting time is estimated. Finally, the effects of control parameters, noise intensity, and the number of control agents on the network synchronization rate are studied. Numerical simulations verify the validity and correctness of the theoretical results.
- complex network,
- stochastic synchronization,
- noise,
- pinning control,
- finite-time control,
- fixed-time control
Citation: Jiaqi Chang, Xiangxin Yin, Caoyuan Ma, Donghua Zhao, Yongzheng Sun. Estimation of the time cost with pinning control for stochastic complex networks[J]. Electronic Research Archive, 2022, 30(9): 3509-3526. doi: 10.3934/era.2022179

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Abstract

In this paper, the finite-time and fixed-time stochastic synchronization of complex networks with pinning control are investigated. Considering the time and energy cost of control, combining the advantages of finite-time control technology and pinning control technology, efficient protocols are proposed. Compared with the existing research, the influence of noise is considered, and sufficient conditions for the network to achieve stochastic synchronization in a finite time are given in this paper. Based on the stability theory of stochastic differential equations, the upper bound of the setting time is estimated. Finally, the effects of control parameters, noise intensity, and the number of control agents on the network synchronization rate are studied. Numerical simulations verify the validity and correctness of the theoretical results.

References

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