Finite-time lag synchronization for two-layer complex networks with impulsive effects

Yao Chu; Xiuping Han; R. Rakkiyappan; Yao Chu; Xiuping Han; R. Rakkiyappan

doi:10.3934/mmc.2024007

Mathematical Modelling and Control

2024, Volume 4, Issue 1: 71-85. doi: 10.3934/mmc.2024007

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Research article

Finite-time lag synchronization for two-layer complex networks with impulsive effects

1.
School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China
2.
Department of Mathematics, Bharathiar University, Coimbatore 641046, Tamilnadu, India

Received: 17 December 2023 Revised: 20 March 2024 Accepted: 22 March 2024 Published: 28 March 2024

This paper mainly considered the finite-time lag synchronization for two-layer complex networks with impulsive effects. Different types of controllers were designed to achieve the lag synchronization of two-layer complex networks. Several sufficient conditions on lag synchronization in the sense of finite time were derived. The time for synchronization was also estimated. It is important to note that synchronization time was influenced by the initial value, as well as the impulses and impulse sequence. This implied that different impulse effects result in varying synchronization times. Additionally, desynchronizing impulses can extend the synchronization time, whereas synchronizing impulses have the opposite effect. Finally, a numerical example was presented to showcase the practicality and validity of the proposed theoretical criteria.
- two-layer complex networks,
- finite-time lag synchronization,
- desynchronizing impulses,
- synchronizing impulses
Citation: Yao Chu, Xiuping Han, R. Rakkiyappan. Finite-time lag synchronization for two-layer complex networks with impulsive effects[J]. Mathematical Modelling and Control, 2024, 4(1): 71-85. doi: 10.3934/mmc.2024007

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Abstract

This paper mainly considered the finite-time lag synchronization for two-layer complex networks with impulsive effects. Different types of controllers were designed to achieve the lag synchronization of two-layer complex networks. Several sufficient conditions on lag synchronization in the sense of finite time were derived. The time for synchronization was also estimated. It is important to note that synchronization time was influenced by the initial value, as well as the impulses and impulse sequence. This implied that different impulse effects result in varying synchronization times. Additionally, desynchronizing impulses can extend the synchronization time, whereas synchronizing impulses have the opposite effect. Finally, a numerical example was presented to showcase the practicality and validity of the proposed theoretical criteria.

References

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