Robustness analysis of exponential synchronization in complex dynamic networks with random perturbations

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

doi:10.3934/math.20231044

AIMS Mathematics

2023, Volume 8, Issue 9: 20487-20509. doi: 10.3934/math.20231044

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Research article

Robustness analysis of exponential synchronization in complex dynamic networks with random perturbations

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

Received: 08 May 2023 Revised: 02 June 2023 Accepted: 12 June 2023 Published: 25 June 2023
MSC : 93B35, 93C73

This article discusses the robustness of exponential synchronization (ESy) of complex dynamic networks (CDNs) with random perturbations. Using the Gronwall-Bellman lemma and partial inequality techniques, by solving the transcendental equation, the maximum perturbation intensity of the CDN is estimated. This implies that the disturbed system achieves ESy if the disturbance intensity is within the range of our estimation. We illustrate the theoretical results with two numerical examples.
- complex dynamic network,
- exponential synchronization,
- random perturbations,
- robustness
Citation: Qike Zhang, Wenxiang Fang, Tao Xie. Robustness analysis of exponential synchronization in complex dynamic networks with random perturbations[J]. AIMS Mathematics, 2023, 8(9): 20487-20509. doi: 10.3934/math.20231044

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Abstract

This article discusses the robustness of exponential synchronization (ESy) of complex dynamic networks (CDNs) with random perturbations. Using the Gronwall-Bellman lemma and partial inequality techniques, by solving the transcendental equation, the maximum perturbation intensity of the CDN is estimated. This implies that the disturbed system achieves ESy if the disturbance intensity is within the range of our estimation. We illustrate the theoretical results with two numerical examples.

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