On dynamics of \(\ell\)-Volterra quadratic stochastic operators. (English) Zbl 1342.92199
Summary: We introduce a notion of \(\ell\)-Volterra quadratic stochastic operator defined on \((m - 1)\)-dimensional simplex, where \(\{0,1,\dots, m\}\). The \(\ell\)-Volterra operator is a Volterra operator if and only if \(\ell = m\). We study structure of the set of all \(\ell\)-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 \(\ell\)-Volterra operators and Volterra ones.
MSC:
| 92D25 | Population dynamics (general) |
| 47B44 | Linear accretive operators, dissipative operators, etc. |
Keywords:
quadratic stochastic operator; fixed point; trajectory; Volterra and non-Volterra operators; simplexReferences:
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