ON DISCRETE-TIME MODELS OF NETWORK WORM PROPAGATION GENERATED BY QUADRATIC OPERATORS
Fatima АdilovaV.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, University str. 9, 100174 Tashkent, UzbekistanUygun JamilovV.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, University str. 9, 100174 Tashkent, Uzbekistan; Akfa University, National Park str. 264, Qibray district, 111221 Tashkent region, Uzbekistan; National University of Uzbekistan, University str. 4, 100174 Tashkent, UzbekistanAndrejs ReinfeldsUniversity of Latvia, Jelgavas str. 3, 1001 Riga, Latvia; Institute of Mathematics and Computer Sciences, Raine Bulvaris 29, 1459 Riga, Latvia
ABI
Abstract
In this paper we consider the discrete-time dynamical systems generated by network worm propagation models based on the theory of quadratic stochastic operators(QSO). This approach simultaneously solves two important problems: exploring of the QSO trajectory‘s behavior, we described the set of limit points, thereby completely solved the main problem of dynamical systems (i), we showed a new application of the theory QSOs in worm propagation modelling (ii). We demonstrated that proposed discrete-time biologically-inspired model represents also realistic picture of the worm propagation process and such analytical models can be used in decision of some problems of computer networks.
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