mathematics Article Fractional Dynamics of Stuxnet Virus Propagation in Industrial Control Systems Zaheer Masood 1, Muhammad Asif Zahoor Raja 2,* , Naveed Ishtiaq Chaudhary 2, Khalid Mehmood Cheema 3 and Ahmad H. Milyani 4 1 Department of Electrical and Electronics Engineering, Capital University of Science and Technology, Islamabad 44000, Pakistan;
[email protected] 2 Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou 64002, Taiwan;
[email protected] 3 School of Electrical Engineering, Southeast University, Nanjing 210096, China;
[email protected] 4 Department of Electrical and Computer Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia;
[email protected] * Correspondence:
[email protected] 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 Citation: Masood, Z.; Raja, M.A.Z.; for the value of a = 1. To understand the depth of fractional model behavior, numerical simulations Chaudhary, N.I.; Cheema, K.M.; are carried out for the distinct order of the fractional derivative system, and the results show that Milyani, A.H.