CONSTRUCTION OF FIXED POINT CARDS FOR DEGENERATE LOTKA-VOLTERRA MAPPINGS

Eshmamatova D. Tadzhieva M. Temirbekov N.
2025 Springer

Journal of Mathematical Sciences (United States)
2025

The paper is devoted to the study of the asymptotic behavior of degenerate Lotka-Volterra mappings operating in a four-dimensional simplex. By now, nondegenerate Lotka-Volterra mappings have been studied, as well as some cases where the second-order principal minors are zero. Here, we have considered a specific operator, which is not an operator in the general position. For mappings of this kind, we suggest a new approach to constructing cards of fixed points since the known method for constructing them is not applicable to the case we are considering. In the paper, all types of cards are constructed for the considered mapping, from tournaments to partially oriented graphs. The operator studied in the paper is interesting because it can be represented as a discrete model of the biogen cycle in an ecosystem.

Card of fixed points , Fixed point , Partially oriented graph , Quadratic Lotka-Volterra mapping , Simplex , Skew-symmetric matrix , Tournament

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Tashkent State Transport University, Tashkent, Uzbekistan
V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan
Al-Farabi Kazakh National University, Almaty, Kazakhstan

Tashkent State Transport University
V.I.Romanovskiy Institute of Mathematics
Al-Farabi Kazakh National University

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