Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)8255Research ArticleInfluence of Stochastization on One-Step ModelsDemidovaA VTelecommunication Systems Departmentavdemidova@sci.pfu.edu.ruGevorkyanM NTelecommunication Systems Departmentmngevorkyan@sci.pfu.edu.ruEgorovA Degorov@im.bas-net.byKulyabovD STelecommunication Systems Departmentdharma@sci.pfu.edu.ruKorolkovaA VTelecommunication Systems Departmentakorolkova@sci.pfu.edu.ruSevastyanovL ATelecommunication Systems Departmentsevast@sci.pfu.edu.ruPeoples’ Friendship University of RussiaInstitute of Mathematics, NASB150120141718508092016Copyright © 2014,2014It is assumed that the introduction of probability in mathematical model makes it more adequate. There are practically no methods of the agreed (depending on structure of the system) introduction of probability in deterministic models. Authors have improved the method of constructing stochastic models for the class of one-step processes and illustrated it by models of population dynamics. Population dynamics was chosen for study because its deterministic models are suﬃciently well explored that allows to compare the obtained results with the results already known. We have examined the impact of the introduction of stochastics in the deterministic model, on the example of population dynamics system of type “predator–prey”. Previously obtained stochastic diﬀerential equations are studied by the methods of the qualitative theory of diﬀerential equations. Stationary state and ﬁrst integral of the system are obtained. To demonstrate the results the numerical simulations on the basis of Runge–Kutta method for stochastic diﬀerential equations are performed. The ﬁrst integral of deterministic system (phase volume) in the stochastic case does not remain unchanged, but increases, which ultimately leads to the death of one or both populations. One of the disadvantages of the classical system of type “predator–prey” is preservation of the amplitude of populations oscillations. In the stochastic model the process terminates with the death of one or both populations, which from the authors’ point of view makes the model more adequate.stochastic differential equations“predator–prey” modelmaster equationFokker–Planck equationстохастические дифференциальные уравнениямодель «хищник–жертва»основное кинетическое уравненияуравнение Фоккера–Планка