Dynamics of separable cubic stochastic operators

This report first presents the basic definitions and concepts of the theory of stochastic operators. Then, the definition of separable cubic stochastic operators defined on a finite-dimensional simplex is provided. Next, the dynamic properties of a single separable cubic stochastic operator defined on a two-dimensional simplex are described. Finally, results on the dynamics of a single separable cubic stochastic operator defined on an $(m-1)$-dimensional simplex are presented.