Про узагальнення однієї математичної моделі дробово-диференціальної динаміки комп’ютерних вірусів
The problem of mathematical and computer modeling of the dynamics of the spread of computer viruses based on the generalization of the fractional-differential model previously published by the authors [1] is considered. The relevance of the considered problem is due to the need to build effective an...
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| Date: | 2025 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
V.M. Glushkov Institute of Cybernetics of NAS of Ukraine
2025
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| Subjects: | |
| Online Access: | https://jais.net.ua/index.php/files/article/view/432 |
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| Journal Title: | Problems of Control and Informatics |
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Problems of Control and Informatics| Summary: | The problem of mathematical and computer modeling of the dynamics of the spread of computer viruses based on the generalization of the fractional-differential model previously published by the authors [1] is considered. The relevance of the considered problem is due to the need to build effective antivirus systems for computer networks based on the results of mathematical modeling the spread of malicious software. In the paper [1], to take into account non-local time effects in the model, a fractional-differential modification with Caputo derivatives of constant order was proposed for the model with ordinary local derivatives from the paper [2]. Within such a framework, closed-form solutions were obtained and a finite-difference scheme of the Adams fractional method was constructed and implemented in software. In contrast, this paper considers a fractional-differential analogue of the model from the paper [1] constructed using the Caputo fractional derivative of both constant and variable orders in the system of equations. Here a technique for solving the problem is developed basing on a combined approach: part of the dependencies was found in a closed form, and the other part — using a numerical technique, as a solution of the corresponding nonlinear Cauchy problem with a variable-order fractional derivative. The results of a qualitative analysis of the correctness conditions for this Cauchy problem are given, as well as some simulation results regarding the fractional dynamics of the spread of computer viruses based on the considered model of computer virology. In particular, the results of numerical experiments show that at small values of the parameter of infection probability for vulnerable computers, the influence of time-non-local effects on the dynamics of infected computers is quite noticeable but, at large values of this parameter, the determining role in the dynamics is played by the influence of the presence of nonlinear component in the corresponding equation. |
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