Journal of Convex Analysis 32 (2025), No. 4, 975--988
Copyright Heldermann Verlag 2025
Dynamics of a Convex Combination and Superposition of Non-Volterra Quadratic Stochastic Operators
Uygun U. Jamilov
(1) V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan
(2) National University of Uzbekistan, Tashkent, Uzbekistan
uygun.jamilov@mathinst.uz
Ramazon T. Mukhitdinov
Department of Mathematics, Institute of Chemical Technology, Tashkent, Uzbekistan
muxitdinov-ramazon@rambler.ru
We consider a convex combination of non-Volterra quadratic stochastic operators defined on the two-dimensional simplex depending on a parameter λ and study their trajectory behaviours. We show that for any λ∈[0, 1] and for any initial point the set of limit points of the trajectory is a singleton. We also prove that a superposition of these non-Volterra quadratic stochastic operators is a regular transformation.
Keywords: Quadratic stochastic operator, Volterra and non-Volterra operator, trajectory.
MSC: 37N25, 92D10.
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