Computer research of nonlinear stochastic models with migration flows

The problems of the design methods extension and computer research of nondeterministic finite-dimensional population models describing migration flows are studied. The significant difficulties arise in the construction of high dimension dynamic models in the course of analytical research. Computer research allows not only to obtain the results of numerical experiments to search for trajectories and estimate the parameters of deterministic models, but also to reveal the effects caused by stochasticization. The model parameters are estimated and local phase portraits are constructed for the initial four-dimensional migration-population model. The transition from the vector ordinary differential equation to the corresponding stochastic differential equation is performed. The structure of the stochastic model is described on the basis of applying the method of constructing self-consistent stochastic models. As a tool for the study of population-migration models, a software package is used to solve numerically the differential equations systems using modified Runge–Kutta methods. The software package allows numerical experiments based on the implementation of algorithms for generating trajectories of multidimensional Wiener processes and multipoint distributions and algorithms for solving stochastic differential equations. The comparative analysis of the computer research results obtained for stochastic models is carried out. The properties of migration-population systems in deterministic and stochastic cases are characterized. The comparison of the results obtained for the three-dimensional and four-dimensional cases is carried out. The effects inherent in models with migration flows are revealed.The obtained results can be applied to the problems of modeling and forecasting the behavior of multidimensional systems describing the migration flows. Copyright © 2019 for the individual papers by the papers’ authors.