R. N. Ganikhodzhaev, M. A. Tadjieva, D. B. Èshmamatova, “Dynamical Properties of Quadratic Homeomorphisms of a Finite-Dimensional Simplex”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2018, Volume 144,Pages <nobr>104

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Dynamical Properties of Quadratic Homeomorphisms of a Finite-Dimensional Simplex

R. N. Ganikhodzhaev^a, M. A. Tadjieva^a, D. B. Èshmamatova^b

^a National University of Uzbekistan named after M. Ulugbek, Tashkent
^b Tashkent Temir YO'L Muxandislari Instituti

Abstract: In this paper, we describe the class of all quadratic homeomorphisms of a finite-dimensional simplex and examine the asymptotic behavior of positive and negative trajectories of such homeomorphisms.

Keywords: quadratic Lotka–Volterra mapping, simplex, tournament, Lyapunov functions, fixed-point chart.

UDC: 517.98

MSC: Primary 37B25; Secondary 37C25, 37C27