Study of Turing patterns in a SI reaction-diffusion propagation system based on network and non-network environments  

作　　者：Yuxuan Tang Shuling Shen Linhe Zhu 

机构地区：[1]School of Mathematical Sciences Jiangsu University,Zhenjiang,212013,P.R.China [2]Department of Stomatology Afiliated Hospital of Jiangsu University Zhenjiang,210008,P.R.China

出　　处：《International Journal of Biomathematics》2024年第1期199-225,共27页生物数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.12002135);Young Science and Technology Talents Lifting Project of Jiangsu Association for Science and Technology.

摘　　要：The study of rumor propagation dynamics is of great significance to reduce.false news and ensure the authenticity of news information.In this paper,a SI reaction-diffusion rumor propagation model with nonlinear saturation incidence is studied.First,through stability analysis,we obtain the conditions for the existence and local stability of the positive equilibrium point.By selecting suitable variable as the control parameter,the critical value of Turing bifurcation and the existence theorem of Turing bifurcation are obtained.Then,using the above theorem and multi-scale standard analysis,the expression of amplitude equation around Turing bifurcation point is obtained.By analyzing the amplitude equation,different types of Turing pattern are divided such as uniform steady-state mode,hexagonal mode,stripe mode and mixed structure mode.Further,in the numerical simulation part,by observing different patterns corresponding to different values of control variable,the correctness of the theory is verified.Finally,the effects of different network structures on patterns are investigated.The results show that there are significant differences in the distribution of users on different network structures.

关 键 词：Reaction-diffusion system rumor propagation amplitude equation Turing pattern 

分 类 号：O17[理学—数学]