Optimal Research On Controllability And Control Energy Of Multiplex Networks

Networks in the real world are often not isolated networks,but are coupled by different networks.For example,the transportation network of human travel is formed by the coupling of aviation network,railway network,public transportation network,etc.In the biomolecular network,there is interlayer coupling in the multiplex biomolecular network composed of the transcriptional regulatory network and the protein-protein interconnection network.The study of multiplex network control problem is also an important content of complex network research.Similar to a isolated network,a multiplex network system is controllable if there is a set of control input signals that enable the network to transite from any initial state to any final state within a limited time.The energy required to drive the multiplex network from the initial state to the final state is the control energy of the system.Since the existence of interlayer coupling in multiplex networks,the coupling characteristics of its edges will have an impact on the control performance of the system.Therefore,this paper analyzes the influence of the connection method between layers in the multiplex networks on the control energy of the network.In particular,for the real multiplex biomolecular network,the optimal problem of its controllability and control energy is investigated in this paper.The main innovations and research contents of this paper are as follows:The influence of the structure of the edges in the multiplex model network on the control energy is explored,and an algorithm that changes the network edges’ direction is used to optimize the network structure,and the change of the network control energy before and after optimization is compared and analyzed.The results show that under the appropriate external input,the control energy required for the controllability of the optimized multiplex network is reduced.At the same time,the influence of the interlayer degree correlation on the controllability and control energy of the multiplex model network is analyzed,and it is found that the network with strong interlayer connection and edge heterogeneity requires less control energy.The method of model network controllability is applied to the real multiplex biomolecular network.Based on the structural characteristics of the molecular network,the distribution of the minimum driver nodes required to realize the controllability of the network in the TRN layer and the PPI layer is analyzed.The essential genes/ pathogen-related genes with important roles in molecular networks are also investigated in the network control.The results show that there is no obvious bias in the distribution of driver nodes at the TRN layer and PPI layer,and the driver nodes tend to avoid essential genes/pathogen-related genes.Furthermore,this paper studies optimal problem of the control energy of biomolecular networks,and finds that the heteromeric structure of the interlayer connection is more conducive to reducing the control energy of the network.At the same time,this paper analyzes and compares the influence of different driver node selection strategies on the network control energy.The results show that selecting essential genes or pathogen-related genes as driver nodes can effectively reduce the control energy.