International Journal of Engineering and Manufacturing (IJEM)
IJEM Vol. 16, No. 3, 8 Jun. 2026
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Mathematical Model of Subpopulation Dynamics in Case of Different Niches for Subpopulations
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Author(s)
O. Kuzenkov
1
M. Tryputen
2
V. Kuznetsov
3,*
O. Huliesha
4
V. Artemchuk
3
Index Terms
Subpopulation, Reproduction, Phase space, Characteristic equation, Singular points, Phase portrait, Jacobian matrix, Attractor, Repeller, Bifurcation, Hypersurface
Abstract
The article presents a model of dynamic processes occurring in non-isolated populations that differ in their habitat and mode of nutrition. The results of theoretical studies carried out on the basis of this model show the decisive influence of the ratio of the coefficients of inter-subpopulation competition on qualitative changes in the behavior of the system and individual subpopulations. This ratio is also the main factor influencing the formation of the dominant subpopulation in the system. It has been shown that the system-wide dynamics of subpopulation processes significantly depends on the reproductive potential of all subpopulations and on the mass fraction of individuals that, according to their phenotypic properties, are related to the parents. In this case, the mass fractions of individuals (transition coefficients) must correspond to the condition of closed system and be in specified intervals. It has been established that subpopulations in real life can exchange descendants, which, in turn, can significantly affect the numerical and qualitative aspects of the dynamics. Using the example of a two-dimensional system, the relationship between the sum of the main elements of the transition coefficient matrix and the mutual dependence of subpopulations, as well as their transition to qualitatively different levels, is shown. The bifurcation properties of the model of subpopulation dynamics with a Lotka–Voltaire type function in basic quality have been studied. An approximate justification of possible bifurcations of the system allows us to evaluate the factors that qualitatively influence the dynamics of the system and develop a number of recommendations to prevent the occurrence of catastrophes and collapses in the system.
Cite This Paper
O. Kuzenkov, M. Tryputen, V. Kuznetsov, O. Huliesha, V. Artemchuk, "Mathematical Model of Subpopulation Dynamics in Case of Different Niches for Subpopulations", International Journal of Engineering and Manufacturing (IJEM), Vol.16, No.3, pp.125-144, 2026. DOI:10.5815/ijem.2026.03.09
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