Classification of a new subclass of $\xi^{(as)}$-QSO and its dynamics

Volume 17, Issue 4, pp 535-544 Publication Date: November 01, 2017       Article History
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Authors

Izzat Qaralleh - Department of Mathematics, Tafila Technical University, P. O. Box 179. zip code 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 subject has not been studied in depth; even QSOs, which are the simplest nonlinear operators, have not been studied thoroughly. In this paper we introduce a new subclass of $\xi^{(as)}$-QSO defined on 2D simplex. first we classify this subclass into 18 non-conjugate classes. Furthermore, we investigate the behavior of one class.

Keywords

• $\ell$-Volterra quadratic stochastic operator
• $\xi^{(s)}$-quadratic stochastic operator
• permuted $\ell$-Volterra quadratic stochastic operator
• dynamics

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

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