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)8602Research ArticleStability Research of Population Dynamics Model on the Basis of Construction of the Stochastic Self-Consistent Models and the Principle of the ReductionDemidovaA VDepartment of Applied Probability and Informaticsavdemidova@sci.pfu.edu.ruDruzhininaO Vovdruzh@mail.ruMasinaO NDepartment of Mathematical Modeling and Computer Technologiesolga121@inbox.ruPeoples’ Friendship University of RussiaInstitution of Russian Academy of Sciences Dorodnicyn Computing Centre of RASYelets State University named after Ivan Bunin150320153182908092016Copyright © 2015,2015The three-dimensional model of interaction of populations taking into account the competition and diﬀusion of species is considered. For research of model the combination of known methods of synthesis and the analysis of models, the principle of a reduction and the developed method of construction of the stochastic self-consistent models is used. Existence conditions of equilibrium states are obtained and the analysis of stability is made. Stability conditions on the basis of the principle of a reduction of a problem about stability of solutions of diﬀerential inclusion to a problem on stability of other types of the equations are oﬀered. The speciﬁed principle assumes transition from the vector ordinary diﬀerential equations to vector diﬀerential inclusion and the fuzzy diﬀerential equation, taking into account change of parameters of diﬀerent types in the studied models. For the considered model of population dynamics synthesis of the corresponding stochastic model on the basis of application of a method of construction of the stochastic self-consistent models is carried out. The structure of stochastic model is described, Fokker-Planck equation is written out, and the rule of transition to the stochastic diﬀerential equation in the form of Langevin is formulated. The oﬀered approach allowed to carry out the comparative analysis of qualitative properties of the models considering the competition and diﬀusion of species in deterministic and stochastic cases. Stability conditions can be used for studying of dynamic behavior of models of population dynamics. The received results are aimed at the further development of methods of construction and the analysis of stability of nondeterministic mathematical models of natural sciences.stochastic modelsingle-step processespopulation dynamicsstabilitydifferential equationsprinciple of a reductionстохастическая модельодношаговые процессыпопуляционная динамикаустойчивостьдифференциальные уравненияпринцип редукции