On Dynamics of ℓ- Volterra Quadratic Stochastic Operators

الأصل · EN

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 iff 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.