Browsing by Author "Kuzenkov, Olexandr"
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Item Mathematical Model of Dynamics of Homomorphic Objects(Petro Mohyla Black Sea National University, Mykolaiv, 2019) Kuzenkov, Olexandr; Serdiuk, Tetiana M.; Kuznetsova, Alisa; Tryputen, Mykola; Kuznetsov, Vitaliy; Kuznetsova, Yevheniia; Tryputen, MaksymENG: 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.Item Nonlinear Analysis of Bifurcatory Properties of Mathematical Model of Subpopulation Dynamics in the Case of a Single Niche for Subpopulation(IEEE, 2022) Kuzenkov, Olexandr; Busher, Victor; Chornyi, Oleksii; Nikolenko, Anatoliy V.; Kuznetsov, Vitaliy V.; Savvin, Oleksandr V.ENG: The article is devoted to the use of mathematical models of the dynamics of heterogeneous populations, and computer simulation based on the above models allows to identify general trends in subpopulations, predict the state of the system and obtain results on possible consequences of artificial intervention. Also, the use of mathematical models can predict the spread of genetic anomalies. The authors propose a model of subpopulation dynamics with a logistic function as a basic one. It is concluded that the system-wide dynamics of subpopulation processes depends not only on the reproductive potential of subpopulations, but also on the intrasystemic dynamics that objectively occur in such systems. The adequacy of the proposed mathematical model is proved. © 2022 IEEE.