CHAOS SYNCHRONIZATION IN A FRACTIONAL-ORDER COMPUTER VIRUS SYSTEM WITH INCOMMENSURATE DYNAMICS

This paper investigates the chaotic dynamics and synchronization of an incommensurate fractional discrete computer virus model. Leveraging fractional calculus captures memory and non-local propagation effects observed in real networks. We characterize the system’s complex behavior using bifurcation diagrams, phase portraits, and the maximum Lyapunov exponent (MLE), confirming chaos via regimes with MLE > 0. We then implement a master–slave coupling to achieve synchronization in the chaotic regime and quantify convergence of the synchronization error. Numerical simulations show that the master system and the slave system synchronize for control parameters f₁ = −0.34, f₂ = −0.52 and f₃ = −0.76. These results highlight how incommensurate fractional orders shape chaotic windows and demonstrate that appropriately tuned feedback can enforce coher-ent behavior, offering insights for designing mitigation strategies against computer-virus spread on complex networks.