Fixed/predefined-time generalized synchronization for stochastic complex dynamical networks with delays

Qike Zhang; Tao Xie; Wenxiang Fang; Qike Zhang; Tao Xie; Wenxiang Fang

doi:10.3934/math.2024266

AIMS Mathematics

2024, Volume 9, Issue 3: 5482-5500. doi: 10.3934/math.2024266

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Research article

Fixed/predefined-time generalized synchronization for stochastic complex dynamical networks with delays

School of Mathematics and Statistics, Hubei Normal University, Hubei, Huangshi 435002, China

Received: 14 December 2023 Revised: 17 January 2024 Accepted: 22 January 2024 Published: 29 January 2024
MSC : 05C82, 93E03

In this paper, the fixed/predefined-time generalized synchronization problem of stochastic complex dynamical networks with delays is studied for the first time. First, based on the feedback controller without linear terms, the results show that the controlled system has strong stability. Second, stochastic analysis methods, inequality techniques, and an extension of the existing fixed/predefined-time stability lemma ($ \eta $ range extension) are used to make the results of this paper more general. The sufficient conditions for generalized synchronization are established, and the settling time independent of the initial values are given. To illustrate the theoretical results, a numerical example is given.
- complex network,
- generalized synchronization,
- fixed-time synchronization,
- predefined-time synchronization
Citation: Qike Zhang, Tao Xie, Wenxiang Fang. Fixed/predefined-time generalized synchronization for stochastic complex dynamical networks with delays[J]. AIMS Mathematics, 2024, 9(3): 5482-5500. doi: 10.3934/math.2024266

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Abstract

In this paper, the fixed/predefined-time generalized synchronization problem of stochastic complex dynamical networks with delays is studied for the first time. First, based on the feedback controller without linear terms, the results show that the controlled system has strong stability. Second, stochastic analysis methods, inequality techniques, and an extension of the existing fixed/predefined-time stability lemma ($ \eta $ range extension) are used to make the results of this paper more general. The sufficient conditions for generalized synchronization are established, and the settling time independent of the initial values are given. To illustrate the theoretical results, a numerical example is given.

References

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