Dynamical System of a Quadratic Stochastic Operator with Two Discontinuity Points

Abstract

We consider a population consisting of two species whose dynamics is determined by a quadratic stochastic operator with variable coefficients, which makes it a discontinuous operator at two points. This operator depends on three parameters. The set of these parameters is divided into seven subsets. For each subset of parameters, we find fixed points, periodic points, and the set of limit points of trajectories generated by the respective quadratic stochastic operators.