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Title: Mathematical Model of Dynamics of Homomorphic Objects
Authors: Kuzenkov, Olexandr
Serdiuk, Tetiana
Kuznetsova, Alisa
Tryputen, Mykola
Kuznetsov, Vytalyi V.
Kuznetsova, Yevheniia
Tryputen, Maksym
Keywords: mathematical model
computer-based simulation
differential model
logistic function
bifurcation characteristics
Issue Date: 2019
Publisher: Petro Mohyla Black Sea National University, Mykolaiv
Citation: Kuzenkov O., Serdiuk T., Kuznetsova A., Tryputen M., Kuznetsov V., Kuznetsova Y., Tryputen M. Mathematical Model of Dynamics of Homomorphic Objects. CEUR Workshop Proceedings. 2019. Vol. 2516 : 1st International Workshop on Information-Communication Technologies and Embedded Systems, ICT and ES 2019, Mykolaiv, Ukraine, 14–15 November 2019. P. 190–205.
Abstract: EN: Abstract. The paper concerns topical problem of mathematical modeling of dynamics of heterogeneous groups with a logistic function as a basic one. Joint use of mathematical models of biological systems and computer-based simulation makes it possible to minimize time and save material resources while determining general tendencies of subpopulation progress; and to forecast state of the system as well as possible consequences of artificial intervention in the environment. Among other things, it concerns forecasting of genetic abnormalities. The paper proposes a model of dynamics of progress of a population consisting of n subpopulations. The model is represented in the form of differential equations with transition coefficients within their right sides. The transition coefficients mirror the share of species getting from ith subpopulation to jth one. The proposed system is not Voltairian one since its phase trajectories may cross coordinate axes. It has been proved that the system of differential equations is degenerated in the neighbourhood of equilibrium points. Analysis of the system of differential equations for n=2 has demonstrated a potential for three bifurcations. It has been proved that nine bifurcation types are possible for n=3. Numerical computer-based experiments have shown that the proposed model is stable as for the disturbance of its coefficients, and the obtained characteristics of the degenerated system are close to real ones.
Description: O. Kuzenkov: ORCID 0000-0002-6378-7993; T. Serdiuk: ORCID 0000-0002-2609-4071; A. Kuznetsova: ORCID 0000-0003-4772-683X; M. Tryputen: ORCID 0000-0003-4523-927X; V. Kuznetsov: ORCID 0000-0002-8169-4598; Y. Kuznetsova: ORCID 0000-0003-2224-8747; M. Tryputen: ORCID 0000-0001-6915-8162
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