Chaos and Complexity in a Fractional Discrete Memristor Based on a Computer Virus Model

In this study, we develop and investigate a novel fractional discrete-time computer virus dynamics model in two dimensions with a memristive nonlinear coupling mechanism. The memristor introduces nonlinearity by having memory regulation that depends on the state and enhances the propagation dynamics of virus spread. By investigating both matching and non-matching fractional orders, it is then possible to derive useful knowledge with respect to cooperating roles in terms of fractional memory and memristive effects. The complexity behind it is confirmed via 3D phase portraits, bifurcation analysis with LEmax calculation, 0–1 chaos test, and SE complexity. Numerical results reveal rich dynamical phenomena, including periodic oscillations, quasi-periodicity, and strong chaos. In fact, positive LEmax values, Brownian-like trajectories, and high-complexity SE corroborate the chaotic nature of the regimes. Thereby, the fractional-order separation in noncommensurate conditions is a marker of chaotic motion, magnified in the emergently high-dimensional space introduced by the memristive element. As these results indicate that the derivative model proposed here provides an excellent fit for complex viruses present in scaffolds, it may prove to be a useful modeling tool.