Advanced Mathematical Models & Applications

ISSN Online: 2519-4445

Advanced Mathematical Models & Applications is a peer-reviewed, open access journal meant to publish original and significant results and articles in all areas of mathematical modeling and their applications. The aim of this Journal is to bring together researchers and practitioners from academia and industry to establishing new collaborations in this area. The Journal will consider for publication also review articles, literature reviews, correspondence concerning views and information published in previous issues.

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Chaos Control and Synchronization in a Fractional-Order Computer Virus System with Incommensurate Dynamics

Published: 03-12-2025

https://doi.org/10.62476/amma.103488

Abstract

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 coherent behavior, offering insights for designing mitigation strategies against computer-virus spread on complex networks.