Research On Robustness Of Two Types Of Multi-layer Networks Under Random And Targeted Attack

Recently,with the rise of high-tech industries,especially the rapid development of technology,the interaction among trade,economy,polities,technology becomes more compact.The nature of a single network cannot depict the real network in the world.The emergence of multiple-layer network has promoted the development of complex network.In this paper,we firstly study the multi-layer interconnected network with two layers under targeted attack by simulation.We set two layer networks are both with poisson degree distribution or power law degree distribution.Firstly,when the two layer networks has same average degree <k>,we study the relationship with the giant component and average degree.Then we keep the average of one layer,and change another average degree to get the function of robustness and the average of one layer.In addition,we also study the relationship with power law index lambda and the robustness.We can find that the average degree and power law index are both positively correlated with robustness of the entire system.We secondly focus on the case of dependent networks with a multiple-to-multiple correspondence of dependent nodes by generalizing feedback and nonfeedback conditions.We develop a new mathematical framework and study numerically and analytically the percolation of dependent networks with partial multiple-to-multiple dependency links by using of percolation theory.From analyzing the process of cascading failure under random attack,the size of the giant component and critical threshold are analytically obtained and testified by simulation results for couple Erd?s-Rényi(ER)networks and Scale-free(SF)networks.The results imply that the system shows a discontinuous phase transition for different coupling strengths.And,we find that the system becomes more resilient and easy to defend by increasing coupling strength and connectivity density.Then,we apply the model to research the robustness of different types of multiple and interdependent networks with multiple dependency links.Finally,we also apply the theories of degree-degree correlation further discuss the robustness of the whole partially interdependent system with multiple-to-multiple relationships and give corresponding analysis and conclusions.