| Issue |
E3S Web Conf.
Volume 193, 2020
International Conference on Modern Trends in Manufacturing Technologies and Equipment (ICMTMTE 2020)
|
|
|---|---|---|
| Article Number | 01051 | |
| Number of page(s) | 10 | |
| Section | Agricultural Science | |
| DOI | https://doi.org/10.1051/e3sconf/202019301051 | |
| Published online | 08 October 2020 | |
Dynamics of competitive interaction between two mining enterprises and one processing: existence and stability of the equilibrium point
1
Saint-Petersburg State University, 7/9 Universitetskaya nab., Saint-Petersburg, 199034, Russia
2
Stavropol State Agrarian University, 12 Zootechnicheskiy Ln, Stavropol, Russia, 355017
* Corresponding author: irina.zaitseva.stv@yandex.ru
A mathematical model of dynamic interaction between two mining enterprises and one processing is formalized and studied in the paper. The process of interaction is described by a system of three delay differential equations. The criterion for asymptotic stability of nontrivial equilibrium point is obtained when all three enterprises co-work steadily. The problem is reduced to finding stability criterion for quasi-polynomial of third order. We found time intervals between deliveries of raw materials and manufacturing of finished products, in which the process of interaction of the three agents is stable.
© The Authors, published by EDP Sciences, 2020
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