On dynamics of quadratic stochastic operators: a survey

We discuss the notion of Volterra, l-Volterra and separable quadratic stochastic operators defined on (m-1)-dimensional simplex, where l∈{0,1,...,m}. The l-Volterra operator is a Volterra operator if and only if l=m. We study the structure of the set of all Volterra and l-Volterra operators and describe their several fixed and periodic points. For m=2 and m=3 we describe behavior of trajectories of (m-1)-Volterra operators. We also mention many remarks with comparisons of l-Volterra operators and Volterra ones. Also we discuss the dynamics of separable quadratic stochastic operators.

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