ON DYNAMICS OF ℓ-VOLTERRA QUADRATIC STOCHASTIC OPERATORS

Аннотация

We introduce a notion of ℓ-Volterra quadratic stochastic operator 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 structure of the set of all ℓ-Volterra operators and describe their several fixed and periodic points. For m = 2 and 3, we describe behavior of trajectories of (m - 1)-Volterra operators. The paper also contains many remarks with comparisons of ℓ-Volterra operators and Volterra ones.

Темы

Идентификаторы

DOI

10.1142/s1793524510000945

Цитирования и источники