Global and local behavior of a class of \(\xi^{(s)}\)-QSO

Volume 10, Issue 9, pp 4834--4845 http://dx.doi.org/10.22436/jnsa.010.09.25

Publication Date: September 17, 2017 Submission Date: September 17, 2016

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Authors

Abdelwahab Alsarayreh - Institute of Engineering Mathematics, University Malaysia, Perlis Pauh Putra Main Campus, 02600 Arau, Perlis, Malaysia. Izzat Qaralleh - Department of mathematics, Faculty of Science, Tafila Technical University, P. O. Box, 179, 66110, Tafila, Jordan. Muhammad Zaini Ahmad - Institute of Engineering Mathematics, University Malaysia, Perlis Pauh Putra Main Campus, 02600 Arau, Perlis, Malaysia. Basma Al-Shutnawi - Department of mathematics, Faculty of Science, Tafila Technical University, P. O. Box, 179, 66110, Tafila, Jordan. Saba Al-Kaseasbeh - Department of mathematics, Faculty of Science, Tafila Technical University, P. O. Box, 179, 66110, Tafila, Jordan.

Abstract

A quadratic stochastic operator (QSO) describes the time evolution of different species in biology. The main problem with regard to a nonlinear operator is to study its behavior. This has not been studied in depth; even QSOs, which are the simplest nonlinear operators, have not been studied thoroughly. This paper investigates the global behavior of an operator taken from \(\xi^{(s)}\)-QSO when the parameter \(a=\frac{1}{2}\). Moreover, we study the local behavior of this operator at each value of \(a,\) where \(0< a < 1\).

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Keywords

• Quadratic stochastic operator
• local behavior
• global behavior.

MSC

•  37E99
•  37N25
•  39B82
•  47H60
•  92D25

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