Convergence of the trajectories of a non-Volterra quadratic stochastic operator

B. J. Mamurov

Bukhara State University, 11 M. Iqbol str., Bukhara, 200118 Republic of Uzbekistan

Abstract: In the present paper we consider non-Volterra quadratic stochastic operators defined on the two-dimensional simplex depending on a parameter $\alpha$. We show that such an operator has a unique fixed point and all the trajectories converge to this unique fixed point.

Keywords: quadratic stochastic operator, Volterra and non-Volterra operator, trajectory, simplex.

UDC: 517.98

Received: 20.11.2023
Revised: 20.11.2023

DOI: 10.26907/0021-3446-2024-10-45-50

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2024, 68:10, 38–42