On Dynamics of Quadratic Stochastic Operators: a Survey
نویسندگان
چکیده
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. Full text
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