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Stability research of nonlinear models population dynamics by means of a divergent method

Keywords:

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


The work is devoted to the stability analysis of nonlinear models population dynamics: «predator–prey–mutualist» model, «competitor–competitor–mutualist» model and «competitor–mutualist–competitor–mutualist» model. Stability study is carried out by a divergent method. The sufficient conditions of uniform stability of equilibrium states are suggested. The analysis of stability of the population models described by the nonlinear differential equations allows to study stability of equilibria states of systems on the basis of divergence properties of vector fields determined by the right parts of the corresponding equations. The obtained results can be used at the solving of stability problems of nonlinear systems. The considered models and conditions of their stability can be used for the solving of problems of modeling of stochastic systems, in particular, for the comparative analysis of qualitative properties of the initial determined models and stochastic models corresponding to them.
References:

 

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