| Issue |
4open
Volume 3, 2020
|
|
|---|---|---|
| Article Number | 10 | |
| Number of page(s) | 8 | |
| Section | Mathematics - Applied Mathematics | |
| DOI | https://doi.org/10.1051/fopen/2020008 | |
| Published online | 28 August 2020 | |
Research Article
Research of a three-dimensional nonlinear dynamic system describing the process of two-level assimilation
Sokhumi State University, Ana Politkovskaia st., Tbilisi, Georgia
* Corresponding author: gia.pochkhua@gmail.com
Received:
9
June
2020
Accepted:
19
July
2020
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.
Key words: Mathematical model / Two-level assimilation / First integral / Cone / Bendixon’s criterion
© T. Chilachava and G. Pochkhua, Published by EDP Sciences, 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.