Turing Instability of Malware Spreading Model with Reaction-diffusion in Cyber-physical System

Considering the nonlinear saturated incidence rate and reaction-diffusion, this paper proposes a SIRS model to characterize the spread of malware in cyber-physical system (CPS). Firstly, the equilibriums and locally asymptotically stability conditions are given by the stability theorem of ordinary differential equation. After introducing diffusion, the Turing instability of the system is examined and the conditions for the appearance of Turing patterns are constructed. Finally, the theoretical analysis is verified by numerical simulation, which reveals that the introduction of reaction-diffusion may induce the Turing instability in CPS.