Dynamical system of a quadratic stochastic operator with two discontinuity points

TL;DR

This paper studies a quadratic stochastic operator with two discontinuity points, modeling a two-species population, and explores conditions for fixed points, convergence, and periodic behavior based on parameter variations.

Contribution

It introduces a novel quadratic stochastic operator with two discontinuities and analyzes its dynamic properties depending on parameters.

Findings

Existence of fixed points under certain parameter conditions

Trajectories may converge or diverge based on parameters

Periodic points can occur in the system

Abstract

In this paper we consider a population consisting of two species, dynamics of which is defined by a quadratic stochastic operator with variable coefficients, making it discontinuous operator at two points. This operator depends on three parameters. It is shown that under suitable conditions on the parameters this operator may have fixed points, convergence of trajectories and there may exist periodic points.