Classification of quadratic stochastic operators
type: Item
instance of: scholarly article
zbMATH Open document ID: 0971.82011
author: I. Kh. Normatov
author: Nasir N. Ganikhodjaev
publication date: 2001-09-24T00:00:00Z
Mathematics Subject Classification ID: 82B20
Mathematics Subject Classification ID: 15A90
zbMATH DE Number: 1651038
zbMATH Keywords: quadratic stochastic operator
zbMATH Keywords: finite-dimensional simplex
zbMATH Keywords: classification
zbMATH Keywords: finite graph
MaRDI profile type: Publication
title: Classification of quadratic stochastic operators
published in: Doklady Akademii Nauk Respubliki Uzbekistan. Matematika, Tekhnicheskie Nauki, Estestvoznanie
review text: Let \(S^{n-1}\) be a finite-dimensional simplex \(S^{n-1}= \{x\in \mathbb{R}^n\mid x_i\geq 0\), \(\sum_{i=1}^nx_i=1\}\) and \(V:S^{n-1}\mapsto S^{n-1}\) be a quadratic stochastic operator \(V(x)_k=\sum_{i,j=1}^nP_{ij,k}x_ix_j\), where \(P_{ij,k}\geq 0\), \(P_{ij,k}=P_{ji,k}\) and \(\sum_{k=1}^n P_{ij,k}=1\) for all \(i,j,k\in\{1,2,\dots,n\}\). The classification of such operators \(V\) constructed on finite graphs is given.
description: scientific article; zbMATH DE number 1651038