Cascading failure in networks with dynamical behavior against multi-node removal

Complex systems in reality can be characterized as networks on which the diverse dynamical behaviors take place. The cascading failure that may cause the disasters triggered by minor events in these dynamic systems is a critical issue needed to reveal. To this end, we introduce a cascading failure model which considers the activity overload when a fraction of nodes is removed in a random way. The average activity and the giant component are derived to evaluate the performance of the network against the cascading failure. The results show the dynamical behavior is a critical factor on the robustness of networks. We found the different characteristics that the network is more robust with biochemical(ℬ), birth-death (ℬD) and regulatory (ℛ) dynamics as the homogeneity of the network increases, but as the heterogeneity of the network increases, the network with epidemic (ℰ) dynamics is more robust. Remarkably, the dynamics with ℬD and ℛ are more sensitive than the dynamics with ℬ and ℰ to the sensitivity factor ρ. It is helpful for the engineer to develop a more robust network with proper measures, especially with limited resources.