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| Synchronization of second-order Kuramoto networks from the perspective of edge dynamics |
| LiangWu1,JiumingZhong1,HaoyongChen2 |
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| (1 School of Physics and Electronic Engineering, Hainan Normal University, Haikou 571158, Hainan, China;2 School of Electric Power, South China University of Technology, Guangzhou 510640, Guangdong, China) |
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| 摘要: |
| This paper presents new synchronization conditions for second-order phase-coupled Kuramoto oscillators in terms of edge
dynamics. Two types of network-underlying graphs are studied, the positively weighted and signed graphs, respectively. We
apply an edge Laplacian matrix for a positively weighted network to represent the edge connections. The properties of the edge
Laplacian matrix are analyzed and incorporated into the proposed conditions. These conditions take account of the dynamics
of edge-connected oscillators instead of all oscillator pairs in conventional studies. For a network with positive and negative
weights, we represent the network by its spanning tree dynamics, and derive conditions to evaluate the synchronization state of
this network. These conditions show that if all edge weights in the spanning tree are positive, and the tree-induced dynamics
are in a dominant position over the negative edge dynamics, then this network achieves synchronization. The theoretical
findings are validated by numerical examples. |
| 关键词: Kuramoto oscillator · Signed graph · Synchronization · Edge Laplacian matrix · Spanning tree |
| DOI：https://doi.org/10.1007/s11768-023-00146-x |
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| 基金项目:This work was partly supported by the Hainan Provincial Natural Science Foundation of China (422RC667). |
|
| Synchronization of second-order Kuramoto networks from the perspective of edge dynamics |
| Liang Wu1,Jiuming Zhong1,Haoyong Chen2 |
| (1 School of Physics and Electronic Engineering, Hainan Normal University, Haikou 571158, Hainan, China;2 School of Electric Power, South China University of Technology, Guangzhou 510640, Guangdong, China) |
| Abstract: |
| This paper presents new synchronization conditions for second-order phase-coupled Kuramoto oscillators in terms of edge
dynamics. Two types of network-underlying graphs are studied, the positively weighted and signed graphs, respectively. We
apply an edge Laplacian matrix for a positively weighted network to represent the edge connections. The properties of the edge
Laplacian matrix are analyzed and incorporated into the proposed conditions. These conditions take account of the dynamics
of edge-connected oscillators instead of all oscillator pairs in conventional studies. For a network with positive and negative
weights, we represent the network by its spanning tree dynamics, and derive conditions to evaluate the synchronization state of
this network. These conditions show that if all edge weights in the spanning tree are positive, and the tree-induced dynamics
are in a dominant position over the negative edge dynamics, then this network achieves synchronization. The theoretical
findings are validated by numerical examples. |
| Key words: Kuramoto oscillator · Signed graph · Synchronization · Edge Laplacian matrix · Spanning tree |
