Fractional-Order Diffusion and Control of Turing Pattern Formation in Malware Propagation for Cyber-Physical Systems

Cyber-physical systems (CPSs) are increasingly integral across modern industries, yet malware proliferation poses significant challenges to their security and stability. This study introduces an advanced model for malware spread that leverages Turing instability and fractional-order diffusion, offering insights into malware propagation dynamics. By developing a 2-D susceptible-infected (SI) model with both self-diffusion and cross-diffusion, we explore the nonlinear interactions influencing malware propagation across CPS nodes. Fractional-order diffusion models are also employed to represent complex, nonlocal propagation, while a state feedback controller is incorporated to manage malware dynamics effectively. The study details conditions for Turing bifurcation and bifurcation thresholds, revealing that changes in the bifurcation parameter influence pattern formations, shifting from hexagonal to stripe formations in malware-infected nodes. Our simulations validate these theoretical insights, demonstrating that the controller and fractional-order diffusion significantly impact malware propagation patterns. This model offers a novel framework for developing malware diffusion control strategies, enhancing cybersecurity resilience in CPSs.