An $(α,β)$- Quadratic Stochastic Operator Acting in $S^2$ - Jamilov, U.U.; Khudoyberdiev, Kh. O. (Journal of Applied Nonlinear Dynamics, 2026)
In the present paper we consider a family of non-Volterra quadratic stochastic operators depending on the parameters $α, β$ and study their trajectory behaviors. We find all fixed and periodic points for an $(α,β)$- quadratic stochastic operator on the two-dimensional simplex. A complete description of the set of limit points is given, and we show that such operators have the ergodic property.