Dynamical aspects of a delayed SEI2RS malware dissemination model in cyber–physical systems

• Published in: Results in physics Vol. 40; p. 105851
• Main Authors: Yu, Xiaodong, Wan, Aying
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.09.2022; Elsevier
• Subjects: Cyber–physical system; Delay; Hopf bifurcation; SEI2RS model; Stability; Stability; Hopf bifurcation; Cyber–physical system; SEI2RS model; Delay
• ISSN: 2211-3797; 2211-3797
• DOI: 10.1016/j.rinp.2022.105851

In current paper, a delayed SEI2RS malware dissemination model in cyber–physical systems is proposed. Effect of the time delay owning to temporary immunity interval of the recovered nodes is analyzed. A series of sufficient criteria determining local stability of malware-existence equilibrium and occurrence of Hopf bifurcation are revealed via regarding the time delay owning to temporary immunity interval of the recovered nodes as bifurcation parameter. Additionally, direction and stability of the Hopf bifurcation are explored with the aid of the center manifold theorem and normal form theory method. At last, numerical calculations are conducted to prove validity of obtained results. •A delayed SEI2RS malware dissemination model in cyber–physical systems is proposed.•Impact of the time delay on the model is analyzed.•Properties of Hopf bifurcation are investigated.•Some suggestions for controlling malware dissemination in cyber–physical systems are presented.