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二分网上的靴襻渗流
Bootstrap percolation on bipartite networks
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摘要: 靴襻渗流最早应用于统计物理学中研究磁铁因非磁性杂质导致磁有序的降低并最终消失的现象．随着复杂网络研究的深入，许多学者展开网络上的靴襻渗流研究．在自然界中，许多系统自然呈现出二分结构，二分网络是复杂网络中的一种重要的网络模式．本文通过建立动力学方程和计算机仿真模拟的方法研究二分网上的靴襻渗流，关注的参数是二分网中两类节点初始的活跃比例和活跃阈值，分别用f1，f2和Ω1，Ω2表示，得到二分网两类节点终态活跃比例随初始活跃比例的变化会发生相变等结论．同时验证了动力学方程与仿真模拟的一致性．Abstract: Bootstrap percolation was first used in statistic physics to study the phenomenon that magnetic-order goes down and disappears because of the disturbance of nonmagnetic impurity. With the development of complex network, the application of bootstrap percolation in network has attracted much attention. In the real world, many systems naturally exhibit the two-branch structure. And bipartite network is one of important networks in complex networks. In this paper, we use the dynamics equation and computational simulation to study the bootstrap percolation in bipartite networks. The parameters we focus on are the node initial active ratios f1 and f2 and active thresholds Ω1, and Ω2. We draw the conclusion that the ratio of active nodes has discontinuous transition, which will gradually disappear with parameters varying. We also prove the consistency between the dynamic equation and simulation results.
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