A Review Of Coarse Graining Methods For Multiscale Dynamics In Complex Networks

In recent years,the method of multi-scale kinetic coarsening on complex networks has attracted great attention and made great progress.Based on the complex network topology and dynamic time-scale separation,a number of multi-scale coarse-grained computational models and simulation methods suitable for different time scales or space scales were established.Firstly,eight kinds of coarse granulation methods are summarized in this paper:geographic coarse granulation,spectral coarse granulation,lattice point coarse granulation,dynamic coarse granulation,Equation-free multi-scale method,renormalization group method,degree(strength)coarse granulation and hybrid multi-scale coarse granulation method.Then,we developed the recently proposed dimension-reduction coarse-granulation method to observe the occurrence of the critical point of the life network,and found that the model after dimension-reduction can predict the critical point of the plant-pollinator reciprocity network,and found the relationship between the occurrence of the critical point and the natural growth rate.Finally,we discuss the problems that still exist in the method of multi-scale coarsening on complex networks and the possible solutions.The main structure of this paper is divided into the following four aspects:Chapter 1: Introduces the background of multi-scale dynamics coarsening method on complex networks and its recent development and common models;Chapter 2: Inductive summary of eight common coarse granulation methods;Chapter 3: Predicting the critical point of the life network with the reduced-dimensional coarse-graining method;Chapter 4: Discuss the deficiencies still existing in the coarse granulation method and throw out the problems that have yet to be solved.