Criteria for the Existence of Internal Fixed Points of Lotka-Volterra Quadratic Stochastic Mappings with Homogeneous Tournaments Acting in an $(m-1)$ - Dimensional Simplex

D.B. Eshmamatova; M.A. Tadhzieva; R.N. Ganikhodhzaev

Journal of Applied Nonlinear Dynamics

Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)

Criteria for the Existence of Internal Fixed Points of Lotka-Volterra Quadratic Stochastic Mappings with Homogeneous Tournaments Acting in an $(m-1)$ - Dimensional Simplex

Journal of Applied Nonlinear Dynamics 12(4) (2023) 679--688 | DOI:10.5890/JAND.2023.12.004

D.B. Eshmamatova, M.A. Tadhzieva, R.N. Ganikhodhzaev

Department of Higher Mathematics of Tashkent State Transport University, Tashkent 100167, Uzbekistan

Department of Algebra and Functional Analysis of the National University of Uzbekistan, Tashkent 100174,

Uzbekistan

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Abstract

It is known, there is a close connection between discrete Lotka-Volterra systems and tournaments. In the paper, we give the concept of a homogeneous tournament, which allows us to obtain new results on the location of fixed points of the Lotka-Volterra systems on the simplex.

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