Nonlinear Dynamics of Discrete-Time Model for Computer Virus Propagation: Chaos, Complexity, Stabilization and Synchronization

This paper investigates a discrete-time compartmental model for computer virus propagation. The model classifies computers into susceptible, latent, and breaking-out states, with nonlinear dynamics driven by infection, recovery, and breakout processes. Stability is analyzed using the basic reproduction number R0, and chaotic behavior is demonstrated through phase portraits, bifurcation diagrams, and maximum Lyapunov exponents. To further characterize complexity, the C0 complexity measure is computed, confirming the richness of the chaotic regime. In addition, control strategies are designed to stabilize the dynamics, and a master–slave synchronization scheme is proposed and validated. Numerical simulations highlight both the complexity and controllability of the system, underscoring its relevance for understanding and mitigating the propagation of computer viruses.