Chaos, control and synchronization in discrete time computer virus system with fractional orders

In this research, we present a novel discrete fractional-order model designed to simulate computer virus propagation. We performed a thorough dynamical analysis, encompassing phase portrait visualization, bifurcation diagram construction, maximal Lyapunov exponent computation, and equilibrium point stability assessment using the basic reproduction number ( $R_0$). To characterize system complexity and validate chaotic dynamics, we employed Approximate Entropy, $C_0$ Complexity, and Permutation Entropy. Furthermore, control and synchronization methodologies were developed to mitigate chaotic behavior and achieve coordinated system dynamics. The findings proved the efficacy of the proposed fractional model in accurately simulating viral spread and illustrated the considerable implications of fractional-order parameters on system dynamics. In order to validate the results, MATLAB simulations were run.