湖北民族大学学报（自然科学版）2024，Vol.42Issue(3)：442-450,9.DOI:10.13501/j.cnki.42-1908/n.2024.09.013
基于复杂网络的谣言传播模型稳定性和最优控制研究
Exploration of Stability and Optimal Control for Rumor Propagation Models within Complex Networks
摘要
Abstract
To gain an in-depth understanding of the laws governing rumor propagation and to explore effective methods of controlling it,an uninformed-susceptible,latent-exposed,spreader-infected,stable-recovered(SEIR)rumor propagation model was constructed based on complex networks,and its dynamic behavior and optimal control problems were investigated.Initially,the next-generation matrix method was utilized to calculate the basic reproduction number,and the local and global asymptotic stability of the rumor-free equilibrium point was discussed using the corresponding Jacobian matrix and the construction of Lyapunov functions.Subsequently,the global asymptotic stability of the rumor-free equilibrium point was proven through the characteristic equation.Finally,the optimal control problem of the model was studied by using the Pontryagin optimal value principle,and the existence and concrete form of the optimal control solution were proved.Additionally,numerical solutions to the optimal control problem were obtained through forward and backward scanning methods.The results indicated that whether a rumor spreads in the system was influenced by the level of network heterogeneity.When the control u=(u) was applied,the objective function reached its minimum,suggesting that controlling the uninformed and latent individuals was effective.This research holds significant importance in the control of rumor propagation.关键词
复杂网络/谣言传播模型/网络异质性水平/稳定性/最优控制/数值模拟Key words
complex network/rumor propagation model/heterogeneity level of the network/stability/optimal control/numerical modeling分类
数理科学引用本文复制引用
庄洪萍,向会立,周敏..基于复杂网络的谣言传播模型稳定性和最优控制研究[J].湖北民族大学学报（自然科学版）,2024,42(3):442-450,9.基金项目
国家自然科学基金项目(ZZG19001). （ZZG19001）
