On the surjectivity of quadratic stochastic operators acting on the simplex

Saburov, Mansoor (2016) On the surjectivity of quadratic stochastic operators acting on the simplex. Mathematical Notes, 99 (3-4). pp. 623-627. ISSN 0001-4346 E-ISSN 1573-8876

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Abstract

It is well-known that a linear stochastic operator (a Markov operator) associated with a square stochastic matrix is a surjection of the simplex if and only if it is bijective. The similar problem was open for nonlinear stochastic operators (nonlinear Markov operators) associated with stochastic hyper-matrices (higher dimensional matrices). In this paper, we solved this problem for quadratic stochastic operators acting on the simplex. Namely, we showed that a quadratic stochastic operator associated with a cubic stochastic matrix is a surjection of the simplex if and only if it is bijective. Moreover, we also described all surjective quadratic stochastic operators of the simplex.

Item Type:	Article (Journal)
Additional Information:	6769/51164
Uncontrolled Keywords:	quadratic stochastic operator, Lotka–Volterra operator, cubic stochastic matrix, surjection, bijection
Subjects:	Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Dr Mansoor Saburov
Date Deposited:	27 Jun 2016 08:23
Last Modified:	22 Dec 2016 14:42
URI:	http://irep.iium.edu.my/id/eprint/51164

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