时滞谣言传播模型的动力学分析  

Dynamic Analysis of a Rumor Propagation Model with Time Delay

作　　者：朱霖河 汤宇轩 ZHU Lin-he;TANG Yu-xuan(School of Mathematical Sciences,Jiangsu University,Zhenjiang 212003,China)

机构地区：[1]江苏大学数学科学学院,江苏镇江212003

出　　处：《数学的实践与认识》2022年第10期250-256,共7页Mathematics in Practice and Theory

摘　　要：研究了一个具有心理调节因子和时滞效应的谣言传播模型首先验证平衡点的存在性;利用谱半径法计算谣言传播的基本再生数。其次通过线性系统特征方程的特征根判断边界平衡点的局部稳定性.进一步,给出了时滞状态下的正平衡点的局部稳定性与发生Hopf分岔的判别条件.最后,通过模拟正平衡点的局部稳定性来验证理论的可靠性。In this paper,we study a rumor propagation model with psychological adjustment factor and time delay.Firstly,the existence of the equilibrium point is verified;the basic reproduction number of rumor propagation is calculated by spectral radius method.Next,we judge the local stability of the disease-free equilibrium point by the characteristic root of the characteristic equation of the linear system.Furthermore,we give the conditions for the local stability of positive equilibrium point and Hopf bifurcation under the state of time delay.Finally,the reliability of the theory is verified by simulating the local stability of the positive equilibriumpoint.

关 键 词：谣言传播 稳定性 时滞 HOPF分岔 

分 类 号：G206[文化科学—传播学] C912.63[经济管理]