Fractional Dynamics of Stuxnet Virus Propagation in Industrial Control Systems

Zaheer Masood, Muhammad Asif Zahoor Raja, Naveed Ishtiaq Chaudhary, Khalid Mehmood Cheema and Ahmad H. Milyani
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Zaheer Masood: Department of Electrical and Electronics Engineering, Capital University of Science and Technology, Islamabad 44000, Pakistan
Muhammad Asif Zahoor Raja: Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou 64002, Taiwan
Naveed Ishtiaq Chaudhary: Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou 64002, Taiwan
Khalid Mehmood Cheema: School of Electrical Engineering, Southeast University, Nanjing 210096, China
Ahmad H. Milyani: Department of Electrical and Computer Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Mathematics, 2021, vol. 9, issue 17, 1-27

Abstract: The designed fractional order Stuxnet, the virus model, is analyzed to investigate the spread of the virus in the regime of isolated industrial networks environment by bridging the air-gap between the traditional and the critical control network infrastructures. Removable storage devices are commonly used to exploit the vulnerability of individual nodes, as well as the associated networks, by transferring data and viruses in the isolated industrial control system. A mathematical model of an arbitrary order system is constructed and analyzed numerically to depict the control mechanism. A local and global stability analysis of the system is performed on the equilibrium points derived for the value of ? = 1. To understand the depth of fractional model behavior, numerical simulations are carried out for the distinct order of the fractional derivative system, and the results show that fractional order models provide rich dynamics by means of fast transient and super-slow evolution of the model’s steady-state behavior, which are seldom perceived in integer-order counterparts.

Keywords: fractional-order virus models; stuxnet virus; numerical computing; supervisory control and data acquisition systems; computer networks; lyapunov analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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