摘要
本文研究具有双线性发生率的SEIR微博舆情传播模型,并考虑复传播情况.基于波动引理、比较原理、Hurwitz判据等方法研究了微博舆情传播模型平衡点的稳定性问题,并以此分析该微博舆情未来传播趋势.当阈值R0<1时,模型仅有舆情消亡平衡点且全局渐近稳定.当阈值R0>1时,模型的舆情消亡平衡点不稳定.另外,给出了当暂未传播率p(t)为分段函数时舆情传播平衡点局部渐近稳定的充分条件.最后,通过数值模拟验证理论结果.
In this paper,we study a kind of SEIR propagation model with bilinear rate and re-spread phenomenon. By using fluctuation lemma,comparison principle and Hurwitz criterion etc.,the stability of the equilibrium is studied for analyzing the future development trend of public sentiment. When R0 〈1,the public sentiment free equilibrium P0 is a unique equilibrium,and it is globally asymptotically stable. When R0〉1,the equilibrium P0 is unstable. In addition,a sufficient condition to guarantee the asymptotic stability of the public sentiment transmission equilibrium P＊is obtained when p（ t） is a step function. Finally,numerical simulation results are in accordance with the theoretical results obtained in this paper.
作者
邵明月
张太雷
刘俊利
SHAO Ming-yue;ZHANG Tai-lei;LIU Jun-li(School of Science, Chang＇an University, Xi＇an 710064, China;School of Science, Xi＇an Polytechnic University, Xi＇an 710048, China)
出处
《湖南师范大学自然科学学报》
CAS
北大核心
2018年第2期88-94,共7页
Journal of Natural Science of Hunan Normal University
基金
中央高校教育教学改革专项经费资助项目(310612176301)
陕西省教育厅科研计划资助项目(16JK1331)
国家自然科学基金资助项目(11401453)
关键词
微博舆情传播
SEIR传播模型
阈值
渐近稳定
数值模拟
public sentiment in micro-blogs
SEIR propagation model
threshold
asymptotically stable
numerical simulation
