Dynamical systems of discontinuous quadratic stochastic operators

In the talk we investigate dynamical systems generated by discontinuous quadratic stochastic operators (QSO). In particular, we investigate the dynamical system of two-dimensional quadratic stochastic operator by reducing it to one-dimensional map with one discontinuity point. Using the Lyapunov exponent, we show that the system is chaotic and present bifurcation diagrams for some values of parameters. Moreover, we consider three-dimensional discontinuous QSO and for some parameter values, we describe the set of limit points.