Bootstrap percolation on bipartite networks

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 f(1) and f(2) and active thresholds Omega(1), and Omega(2). 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.