Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Uygun Jamilov

V. I. Romanovskiy Institute of Mathematics, Academy of Sciences, 100170 Tashkent, Uzbekistan

jamilovu@yandex.ru

Andrejs Reinfelds

Institute of Mathematics and Computer Sciences, University of Latvia, Rīga, Latvia
and: Faculty of Physics, Mathematics and Optometry, University of Latvia, Rīga, Latvia

andrejs.reinfelds@lu.lv

Keywords

  • Quadratic stochastic operator
  • Volterra operator
  • cubic stochastic operator

Mathematics Subject Classification

37N25; 92D10

Suggested citation

U. Jamilov, A. Reinfelds. “A Family of Volterra Cubic Stochastic Operators.” Journal of Convex Analysis 28 (2021), No. 1, 19–30. https://doi.org/10.68381/jca28003

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Published by Heldermann Verlag, 2021. Rights now held by Banach Press.