O.V. Druzhinina - Dr.Sc. (Phys.-Math.), Professor, Chief Research Scientist, FRC «Computer Science and Control» of RAS (Mocsow). E-mail: ovdruzh@mail.ru O.N. Masina - Dr.Sc. (Phys.-Math.), Head of of Department Mathematical Modeling and Computer Technologies, Yelets State University named after I.A. Bunin. E-mail: olga121@inbox.ru A.V. Shcherbakov - Post-graduate Student, Department Mathematical Modeling and Computer Technologies, Yelets State University named after I.A. Bunin. E-mail: shcherbakov_al.vl@mail.ru

The structure is described, systematization is carried out and the review of results of research of two-dimensional, three-dimensional and four-dimensional models of dynamics of populations with the mutualism relations is given. Qualitative analysis of the model which describes the interaction between a predator, the prey and a mutualist is made and also the model which is characterized by existence of two species-competitors interacting among themselves, each of which interacts also with a species-mutualist is considered. The equilibrium states are founded, the stability analysis is made and the appropriate phase portraits are constructed. Transition from the nonlinear multidimensional differential equations describing models of population dynamics to vectorial differential inclusion, and to fuzzy and stochastic differential equations is considered. The comparative analysis of properties of models is performed by means of the principle of reduction. The obtained results can be used in the solving of problems of construction and stability analysis of nondeterministic models of nonlinear dynamics.

 

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