An issue which is increasingly attracting attention from scientists to engineers, is the robustness of networks which is the ability against perturbations. It is found that both the network topology and network dynamics affect the robustness of networks. In this article, we present the cascading failure model triggered by perturbing a fraction $1-p$ of nodes on SF networks with three dynamics: the biochemical($\mathcal{B}$), epidemic($\mathcal{E}$) and regulatory($\mathcal{R}$) dynamics. A mathematical method is developed to calculate the cascading failure size and the giant component to evaluate the robustness when a fraction $1-p$ of nodes is perturbed on SF dynamical networks. We perform extensive numerical simulations to test and verify this formula and find that the theoretical results are in good agreement with simulations. The results show that the network is more robust as the tolerance coefficient $\delta$ increases, and the size of network has little influence on the robustness, especially for $\mathcal{B}$ and $\mathcal{R}$. Remarkably, the heterogeneity of networks is positive on the robustness. Moreover, the different characteristics that as the parameter $B$ increases or the parameter $R$ decreases the network with $\mathcal{B}$ is more robust, and as the parameter $R$ increases or the parameter $B$ decreases the network with $\mathcal{E}$ and $\mathcal{R}$ is more robust are found. These findings may be useful for engineers to improve the robustness of the network or design robust networks with dynamics.

越来越引起科学家和工程师关注的一个问题是网络的鲁棒性，即抗扰动的能力。发现网络拓扑和网络动态都会影响网络的鲁棒性。在本文中，我们介绍了由扰动分数触发的级联故障模型$1-磷$ SF 网络上的节点具有三个动态：生化（$\mathcal{乙}$）， 流行病（$\mathcal{乙}$) 和监管 ($\mathcal{电阻}$) 动态。开发了一种数学方法来计算级联故障大小和巨型组件，以评估当分数为$1-磷$节点数在 SF 动态网络上受到干扰。我们进行了大量的数值模拟来测试和验证这个公式，并发现理论结果与模拟非常吻合。结果表明，随着容差系数的增加，网络更加鲁棒$\delta$ 增加，网络规模对鲁棒性影响不大，特别是对于 $\mathcal{乙}$ 和 $\mathcal{电阻}$. 值得注意的是，网络的异构性对鲁棒性是积极的。此外，作为参数的不同特性$乙$ 增加或参数 $\mathrm{电阻}$ 减少网络 $\mathcal{乙}$ 更稳健，并且作为参数 $\mathrm{电阻}$ 增加或参数 $乙$ 减少网络 $\mathcal{乙}$ 和 $\mathcal{电阻}$发现更健壮。这些发现可能有助于工程师提高网络的鲁棒性或设计具有动力学的鲁棒网络。