The diffusion and bootstrap percolation models were studied in regular random and Erdős-Rényi networks using the modified Newman-Ziff algorithms. We calculated the percolation threshold and the order parameter of the percolation transition (strength of the giant cluster) and its derivatives. The percolation transitions are classified by the results. The diffusion percolation with a small k has a double transition, and the bootstrap percolation with $m\ge 3$ has the first-order percolation transition. The diffusion percolation with a large k and the bootstrap percolation with a small m show the second-order percolation transition. Particularly, third-order percolation transitions were discovered in the bootstrap percolation of $m=2$ in regular random networks.

使用改进的 Newman-Ziff 算法在常规随机和 Erdős-Rényi 网络中研究了扩散和自举渗透模型。我们计算了渗透阈值和渗透转变的阶参数（巨星团的强度）及其导数。渗流转变按结果分类。具有小k的扩散渗流具有双重过渡，而自举渗流具有$米\ge 3$具有一阶渗透跃迁。大k的扩散渗流和小m的自举渗流显示了二阶渗流转变。特别是，在自举渗流中发现了三阶渗流转变$米=2$ 在常规随机网络中。