Clustering dynamics of nonlinear oscillator network: Application to graph coloring problem |
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Authors: | Jianshe Wu Licheng Jiao Rui Li Weisheng Chen |
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Institution: | The Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education of China, 2# Taibai South Road, Xidian University, Xi’an 710071, PR China |
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Abstract: | The Kuramoto model is modified by introducing a negative coupling strength, which is a generalization of the original one. Among the abundant dynamics, the clustering phenomenon of the modified Kuramoto model is analyzed in detail. After clustering appears in a network of coupled oscillators, the nodes are split into several clusters by their phases, in which the phases difference within each cluster is less than a threshold and larger than a threshold between different clusters. We show that this interesting phenomenon can be applied to identify the complete sub-graphs and further applied to graph coloring problems. Simulations on test beds of graph coloring problems have illustrated and verified the scheme. |
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Keywords: | Clustering Graph coloring Phase oscillator Complement graph Kuramoto model |
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