Modeling the dynamics of information propagation in the temporal and spatial environment  

作　　者：Yi Zhang Linhe Zhu 

机构地区：[1]School of Mathematical Sciences,Jiangsu University,Zhenjiang,212013,China

出　　处：《Communications in Theoretical Physics》2023年第9期22-35,共14页理论物理通讯（英文版）

基　　金：partly supported by the National Natural Science Foundation of China (Grant No. 12002135);China Postdoctoral Science Foundation (Grand No. 2023M731382);the Young Science and Technology Talents Lifting Project of Jiangsu Association for Science and Technology。

摘　　要：In this paper, we try to establish a non-smooth susceptible–infected–recovered(SIR) rumor propagation model based on time and space dimensions. First of all, we prove the existence and uniqueness of the solution. Secondly, we divide the system into two parts and discuss the existence of equilibrium points for each of them. For the left part, we define R_(0) to study the relationship between R_(0) and the existence of equilibrium points. For the right part, we classify many different cases by discussing the coefficients of the equilibrium point equation. Then, on this basis, we perform a bifurcation analysis of the non-spatial system and find conditions that lead to the existence of saddle-node bifurcation. Further, we consider the effect of diffusion. We specifically analyze the stability of equilibrium points. In addition, we analyze the Turing instability and Hopf bifurcation occurring at some equilibrium points. According to the Lyapunov number, we also determine the direction of the bifurcation. When I = I_(c), we discuss conditions for the existence of discontinuous Hopf bifurcation. Finally, through numerical simulations and combined with the practical meaning of the parameters, we prove the correctness of the previous theoretical theorem.

关 键 词：non-smooth system rumor propagation Turing instability Hopf bifurcation 

分 类 号：O17[理学—数学]