Partial synchronization in community networks based on the intra- community connections

Jianbao Zhang; Xiangyong Chen; Jinde Cao; Jianlong Qiu; Jianbao Zhang; Xiangyong Chen; Jinde Cao; Jianlong Qiu

doi:10.3934/math.2021385

AIMS Mathematics

2021, Volume 6, Issue 6: 6542-6554. doi: 10.3934/math.2021385

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Research article

Partial synchronization in community networks based on the intra- community connections

1.
School of Mathematics, Southeast University, Nanjing 210096, China
2.
School of Information Science and Engineering, Linyi University, Linyi 276005, China
3.
Yonsei Frontier Lab, Yonsei University, Seoul 03722, South Korea
4.
School of Automation, Southeast University, Nanjing 210096, China

Received: 29 January 2021 Accepted: 08 April 2021 Published: 15 April 2021
MSC : 05C82, 34D06

In this paper, we propose a novel criterion on the partial synchronization in a generalized linearly coupled network by employing Lyapunov stability theory and linear matrix inequality. The obtained criterion is only dependent on intra-community connections, and the information of inter-community connections is not necessary. Therefore, it provides more convenience in reducing network sizes in practice. Compared with the previous classical criterion, the threshold derived from the obtained criterion is no less than the classical threshold. We give some particular cases in which the obtained threshold is equal to the classical threshold. Finally, we show numerical simulations to verify the validity of the proposed criteria and comparisons.
- community network,
- partial synchronization,
- invariant manifold,
- intra-community connection
Citation: Jianbao Zhang, Xiangyong Chen, Jinde Cao, Jianlong Qiu. Partial synchronization in community networks based on the intra- community connections[J]. AIMS Mathematics, 2021, 6(6): 6542-6554. doi: 10.3934/math.2021385

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Abstract

In this paper, we propose a novel criterion on the partial synchronization in a generalized linearly coupled network by employing Lyapunov stability theory and linear matrix inequality. The obtained criterion is only dependent on intra-community connections, and the information of inter-community connections is not necessary. Therefore, it provides more convenience in reducing network sizes in practice. Compared with the previous classical criterion, the threshold derived from the obtained criterion is no less than the classical threshold. We give some particular cases in which the obtained threshold is equal to the classical threshold. Finally, we show numerical simulations to verify the validity of the proposed criteria and comparisons.

References

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