On incommensurate chaotic fractional discrete model of computer virus: stabilization and synchronization

Omar Kahouli; Imane Zouak; Ma'mon Abu Hammad; Adel Ouannas; Mohamed Ayari; Omar Kahouli; Imane Zouak; Ma'mon Abu Hammad; Adel Ouannas; Mohamed Ayari

doi:10.3934/math.2025890

AIMS Mathematics

2025, Volume 10, Issue 8: 19940-19957. doi: 10.3934/math.2025890

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On incommensurate chaotic fractional discrete model of computer virus: stabilization and synchronization

1.
Department of Electronics Engineering, Applied College, University of Ha'il, Ha'il 2440, Saudi Arabia
2.
System Dynamics and Control Laboratory, Department of Mathematics and Informatics, University of Larbi Ben M'hidi, Oum El Bouaghi 04000, Algeria
3.
Department of Mathematics, Al-Zaytoonah University of Jordan, Amman 11733, Jordan
4.
Department of Mathematics and Computer Sciences, University of Larbi Ben M'hidi, Oum El Bouaghi 04000, Algeria
5.
Department of Information Technology, Faculty of Computing and Information Technology, Northern Border University, Arar 91431, Saudi Arabia

Received: 02 July 2025 Revised: 19 August 2025 Accepted: 21 August 2025 Published: 29 August 2025
MSC : 34H10, 37N99, 93C55, 93D15, 94C99

The chaotic propagation of computer viruses presents a significant challenge in cybersecurity, necessitating advanced mathematical models for understanding and controlling their spread. In this study, we investigate the stabilization and synchronization of chaos in a fractional-order discrete computer virus model with incommensurate order. We begin by analyzing the chaotic behavior of the incommensurate fractional virus model, thereby employing tools such as bifurcation diagrams, phase portraits, and Lyapunov exponents to characterize its nonlinear dynamics. The results reveal that the system exhibits chaotic behavior under specific parameter conditions, which results in unpredictable virus spread. To mitigate these chaotic effects, we implement stabilization strategies aimed at stabilizing the system and suppressing chaotic outbreaks. Additionally, we explore synchronization techniques, which are of paramount importance in understanding virus interactions within networked systems. Numerical results are presented to corroborate the theoretical findings presented in this paper.
- computer virus model,
- incommensurate order,
- chaos,
- control,
- synchronization
Citation: Omar Kahouli, Imane Zouak, Ma'mon Abu Hammad, Adel Ouannas, Mohamed Ayari. On incommensurate chaotic fractional discrete model of computer virus: stabilization and synchronization[J]. AIMS Mathematics, 2025, 10(8): 19940-19957. doi: 10.3934/math.2025890

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Abstract

The chaotic propagation of computer viruses presents a significant challenge in cybersecurity, necessitating advanced mathematical models for understanding and controlling their spread. In this study, we investigate the stabilization and synchronization of chaos in a fractional-order discrete computer virus model with incommensurate order. We begin by analyzing the chaotic behavior of the incommensurate fractional virus model, thereby employing tools such as bifurcation diagrams, phase portraits, and Lyapunov exponents to characterize its nonlinear dynamics. The results reveal that the system exhibits chaotic behavior under specific parameter conditions, which results in unpredictable virus spread. To mitigate these chaotic effects, we implement stabilization strategies aimed at stabilizing the system and suppressing chaotic outbreaks. Additionally, we explore synchronization techniques, which are of paramount importance in understanding virus interactions within networked systems. Numerical results are presented to corroborate the theoretical findings presented in this paper.

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