Research On Controllability Of Interdependent Networks Under Cascading Failure

Complex networks are ubiquitous in the world,the primary task of researching complex networks is abstracting the actual network as a network model consisting of nodes and edges,according to the model,its topological structure and dynamic behavior are studied.The ultimate goal of the research network is to better control the network,that is,how to apply a control signal to a part of the nodes in the network so that all the nodes in the network can reach our desired state.To control the network,the first is to determine whether the network is controlled or not,therefore,it is great significance to research the controllability of complex networks to realization of network control.A paper on the controllability of complex network structures has been published in Nature,which has attracted the attention of many researchers.This paper proposes a controllability analysis framework,which uses the theory of linear system structure controllability and solves the minimum driving node set based on the maximum matching method.The research on the control of complex network systems has gradually been valued by people and has become a hot topic in the research of complex networks.First of all,we make a phased summary of the research status to the complex networks,cascading failures of interdependent networks and the controllability of complex networks,besides,the basic concepts of complex networks,the basic topology models used in the research of complex networks and the controllability theories of complex networks are described in detail,these provide reference for future research work.Secondly,a directed interdependent network controllability model is constructed for different dependent proportions,we research the controllability of the interdependent network under the absence of cascading failures and the existence of cascading failures.By attacking different proportion of single network nodes,we found that under the absence of cascading failures,increasing the interdependent proportion of network will enhance the controllability of the network no matter what proportion of attacks.However,the simulation results show two kinds of phenomena when we consider the cascading failure.On the one hand,the controllability of the network decreases with increasing the interdependent proportion under any proportion of attacks when the interdependent proportion is smaller,this conclusion is the opposite of without cascading failure.On the other hand,there are two trends as the proportion of attack is different when the interdependent proportion is larger,and there is a threshold of attack proportiona ??0.4,The controllability of the network is getting better and better as the interdependent proportion increases whena ???_c,the controllability of the network gradually decreases with the increase in interdependent proportion as ???_c.Subsequently,these two conclusions of cascading failures are verified by simulation analysis.Finally,in order to enhance the controllability of directed interdependent networks under cascading failure,we construct a cascading failure controllability model with directed interdependent network,and propose two parameters of node protection proportion F and node protection strength S,and five kinds of node protection strategies.Through the simulation and comparison,it is found that the increase of F and S will enhance the controllability of the network,the protection strategies of four different degree nodes are better than the random protection strategy,and the effect of these four protection strategies is very close.We also found that the impact of F and S on controllability of network is very close,the controllability of the network will be better if these two parameters are closer when the total extent of protection is the same.The research provides a reference for how to improve the controllability of cascaded failures in directed interdependent networks.