Journal of Convex Analysis 28 (2021), No. 1, 019--030
Copyright Heldermann Verlag 2021
A Family of Volterra Cubic Stochastic Operators
V. I. Romanovskiy Institute of Mathematics, Academy of Sciences, 100170 Tashkent, Uzbekistan
Institute of Mathematics and Computer Sciences, University of Latvia, Riga, Latvia
and: Faculty of Physics, Mathematics and Optometry, University of Latvia, Riga, Latvia
We consider a convex combination of Volterra cubic stochastic operators defined on a two-dimensional simplex depending on the parameter θ and study their trajectory behaviours. We show that at the values θ = 0.5 the trajectories change their orientation. Moreover, for θ small than 0.5 any Volterra cubic stochastic operator has the property being regular and it is non-ergodic while θ is greater than 0.5.
Keywords: Quadratic stochastic operator, Volterra operator, cubic stochastic operator.
MSC: 37N25; 92D10.
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