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.

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, Riga, Latvia
and: Faculty of Physics, Mathematics and Optometry, University of Latvia, Riga, Latvia

andrejs.reinfelds@lu.lv

U. Jamilov, A. Reinfelds. “A Family of Volterra Cubic Stochastic Operators.” Journal of Convex Analysis 28 (2021), No. 1, 19–30.