A class of two-sex population quadratic stochastic operators: b-bistochastic-volterra

Abstract

This paper aims to investigate the simplest non-linear Markov operators which is the quadratic. Study of quadratic stochastic operators (QSOs) is not an easy task as linear operators. Thus, researchers introduced classes of QSOs such as Volterra QSOs, strictly non-Volterra QSOs, Orthogonal preserving QSOs, Centered QSOs etc. However, all the introduced classes were not yet cover the whole set of QSOs. Therefore, we introduce a new class of QSOs, namely b-bistochastic-Volterra QSOs or simply bV-QSOs. In this paper, we describe the canonical form of bV-QSO on two-dimensional simplex. This helps understanding the dynamical behaviours of bV-QSOs for future works.