On the Dynamics of a Quasi-Strictly Non-Volterra Cubic Stochastic Operator

Summary: In this study, we examine cubic stochastic operators, which we will refer to as quasi-strictly non-Volterra cubic operators. Firstly, the definition of a quasi-strictly non-Volterra operator is provided, and the structure of an arbitrary quasi-strictly non- Volterra cubic operator on a two-dimensional simplex S2 is described. Secondly, the fixed and limit points of the quasi-strictly non-Volterra operator on S2 are investigated. It is proven that there exists a repelling unique fixed point.