新疆师范大学学报（自然科学版）2026，Vol.45Issue(3)：91-101,112,12.
基于PD控制的一类考虑有限治疗资源的时滞扩散恶意软件传播模型
A Delay-diffusion Malware Propagation Model with Limited Treatment Resources based on PD Control
摘要
Abstract
In order to investigate the spatial-temporal dynamic propagation characteristics of malware in the Internet of Things system,this paper establishes a delay-diffusion malware propagation model with limited treatment resources based on the theory of differential equations.By analyzing the relevant characteristic equations,the conditions for Turing instability and Hopf bifurcation are derived.To enhance the system stability,Proportional-Derivative(PD)control is introduced into the model,and the stability of the controlled model is analyzed.Numerical simulations confirm the correctness of the theoretical derivations and demonstrate that the occurrence of Turing instability and Hopf bifurcation can be controlled by choosing appropriate parameters of the PD controller.关键词
物联网/恶意软件/时滞扩散/有限治疗资源/PD控制Key words
Internet of Things/Malware/Delay-diffusion/Limited treatment resources/PD control分类
数理科学引用本文复制引用
郭佳,李婷,王怀柱..基于PD控制的一类考虑有限治疗资源的时滞扩散恶意软件传播模型[J].新疆师范大学学报（自然科学版）,2026,45(3):91-101,112,12.基金项目
宁夏自然科学基金项目(2025AAC030163) （2025AAC030163）
宁夏自然科学基金项目(2024AAC03038) （2024AAC03038）
国家自然科学基金资助项目(72461029). （72461029）
