Modeling the dynamics of the spread of computer viruses using compositions of Lotka–Volterra mappings
Keywords:
Lotka mapping–Volterra, graph, tournament, mixed graph, degenerate skew-symmetric matrix, non-degenerate skew-symmetric matrix, repeller, attractorAbstract
Computer virology and its formalization began seventy years ago with the work of Alan Turing. The work and results of von Neumann, Fred Cohen, Leonard Adleman, and others who followed them were groundbreaking. They provide a solid foundation for computer virology. The theoretical results proposed in the works of these scientists are very important, both when considering the attacking side – viruses and other malware, and when considering on the opposite side: protection and antiviral control. However, as it turned out, such formalization is still far away. The formal work of mathematicians in the 1930s greatly contributed to the development of viruses. A number of virus writers have discovered a huge field of application of this formalization. This theoretical formalization helped to model and understand the opposite face of computer virology, that is, the fight against antiviral drugs. From the very beginning of computer virology, the choice of scanning as the main antivirus method was dictated not so much by pragmatism as by theoretical considerations and results. In connection with the above facts, the paper proposes a different model based on the composition of the Lotka – Volterra operators, which is able to describe the dynamics of virus programs capable of running in different operating systems simultaneously for multiplying viruses and for the case when viruses are of a replicative nature.
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