*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 <sup>3</sup> and Ahmad H. Milyani <sup>4</sup>**


**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 *α* = 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
