Dynamics of superposition of non-volterra quadratic stochastic operators

In this talk, we begin by recall essential definitions and concepts from the theory of stochastic operators. Then we present results regarding the dynamics of a stochastic operator formed by the superposition of two quadratic stochastic operators corresponding to permutations on small-dimensional simplices. Next, we discuss the superposition of regular and ergodic quadratic stochastic operators defined on the two-dimensional simplex. Finally, we give the results on the dynamical systems generated by stochastic operators that are superpositions of extremal Volterra and permuted Volterra quadratic stochastic operators defined on the two-dimensional simplex.