Analysis on the evolution process of BFW-like model with discontinuous percolation of multiple giant components
Analysis on the evolution process of BFW-like model with discontinuous percolation of multiple giant components
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DOI：
10.1016/j.physa.2012.11.033
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发表时间：
2012-06
影响因子：
3.3
通讯作者：
Renquan Zhang;Wei Wei-Wei;Binghui Guo;Yang Zhang;Zhiming Zheng
中科院分区：
文献类型：
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作者：
Renquan Zhang;Wei Wei-Wei;Binghui Guo;Yang Zhang;Zhiming Zheng
最近，随机图上的修正BFW模型[W. Chen，R. M. D'Souza，Phys. Rev. Lett. 106（2011）115701]，其显示了具有多个巨组分的不连续渗流转变，引起了物理学家和统计学家的极大关注。本文通过建立改进的BFW模型的演化方程，分析了随机图和有限维格子上的演化过程和稳态。在随机图上，通过改变边接受率α，系统在巨连通分支数不同的情况下稳定在稳态.此外，在稳态下，α值与巨分量数之间建立了密切的对应关系，数值模拟验证了这种方法的有效性.然后，通过求解由演化方程导出的约束条件，得到不同演化策略下巨分支的大小。同时，将类似的分析扩展到有限维格点，发现有限维格点上的BFW（α）模型与随机图上的BFW（α）模型具有不同的稳态，但它们具有相同的演化机制.对非连续渗流演化过程和稳态的分析有助于解释非连续渗流的性质和非局域性的作用。
Recently, the modified BFW model on random graphs [W. Chen, R.M. D’Souza, Phys. Rev. Lett. 106 (2011) 115701], which shows a discontinuous percolation transition with multiple giant components, has attracted much attention from physicists and statisticians. In this paper, by establishing the evolution equations on the modified BFW model, the evolution process and steady-states on both random graphs and finite-dimensional lattices are analyzed. On a random graph, by varying the edge accepted rate α, the system stabilizes in a steady-state with different numbers of giant components. Moreover, a close correspondence is built between the values of α and the number of giant components in steady-states, the efficiency of which is verified by the numerical simulations. Then, the sizes of giant components for different evolution strategies can be obtained by solving some constraints derived from the evolution equations. Meanwhile, a similar analysis is expanded to finite-dimensional lattices, and we find the BFW (α) model on a finite-dimensional lattice has different steady-states from those on a random graph, but they have the same evolution mechanism. The analysis of the evolution process and steady-state is of great help to explain the properties of discontinuous percolation and the role of nonlocality.