摘要We study a spatial rock-scissors-paper model in a square lattice and a quenched small-world network. The system exhibits a global oscillation in the quenched small-world network, but the oscillation disappears in the square lattice. We find that there is a local oscillation in the square lattice the same as in the quenched small-world network. We define σ=1/NΣi(di-<di>)2 (where di is the density of a kind of species and <di> is the average value) as the variance of the oscillation amplitude in a certain local patch. It is found that σ decays in a power law with an increase of the local patch size R in the square lattice σ∝ R-δ, but it remains constant with an increase of the patch size in the quenched small-world network. We can speculate that in the square lattice, superposition between the local oscillations in different patches leads to global stabilization, while in the quenched small-world network, long-range interactions can synchronize the local oscillations, and their coherence results in the global oscillation.
Abstract：We study a spatial rock-scissors-paper model in a square lattice and a quenched small-world network. The system exhibits a global oscillation in the quenched small-world network, but the oscillation disappears in the square lattice. We find that there is a local oscillation in the square lattice the same as in the quenched small-world network. We define σ=1/NΣi(di-<di>)2 (where di is the density of a kind of species and <di> is the average value) as the variance of the oscillation amplitude in a certain local patch. It is found that σ decays in a power law with an increase of the local patch size R in the square lattice σ∝ R-δ, but it remains constant with an increase of the patch size in the quenched small-world network. We can speculate that in the square lattice, superposition between the local oscillations in different patches leads to global stabilization, while in the quenched small-world network, long-range interactions can synchronize the local oscillations, and their coherence results in the global oscillation.
SUN Rong-Sheng;HUA Da-Yin. Synchronization of Local Oscillations in a Spatial Rock-Scissors-Paper Game Model[J]. 中国物理快报, 2009, 26(8): 86403-086403.
SUN Rong-Sheng, HUA Da-Yin. Synchronization of Local Oscillations in a Spatial Rock-Scissors-Paper Game Model. Chin. Phys. Lett., 2009, 26(8): 86403-086403.
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2009, Vol. 26 
