Abstract
The work proposes a new general nonlinear mathematical model describing the social process of two-level assimilation taking into account quadratic members of self-restriction of population growth of three sides. In the case of constant coefficients of the model, the first integral of a three-dimensional dynamic system has been found, which in the phase space of solutions is a cone. The three-dimensional dynamic system is reduced to two-dimensional and with the help of the Bendixon’s criterion the theorem of existence in the first quarter of the phase plane of the closed integral trajectory is proved. Thus, conditions on model parameters are found that do not fully assimilate the third side.
Highlights
One of the most sought-after directions of applied mathematics is mathematical modeling
Creation of mathematical models is more original in social sphere, because, they are more difficult to substantiate
We created a new direction of mathematical modeling, i.e. “Mathematical Modeling of Information Warfare” [15–17]
Summary
Abstract – The work proposes a new general nonlinear mathematical model describing the social process of two-level assimilation taking into account quadratic members of self-restriction of population growth of three sides. In the case of constant coefficients of the model, the first integral of a three-dimensional dynamic system has been found, which in the phase space of solutions is a cone. The three-dimensional dynamic system is reduced to two-dimensional and with the help of the Bendixon’s criterion the theorem of existence in the first quarter of the phase plane of the closed integral trajectory is proved. Conditions on model parameters are found that do not fully assimilate the third side
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