Dynamics of a population with two equal dominated species

In this talk we consider a population with two equal dominated species, dynamics of which is defined by an one-dimensional piecewise-continuous, two parametric function. It is shown that for any non-zero parameters this function has two fixed points and several periodic points. We proved that all periodic (in particular fixed) points are repelling, and found an invariant set which asymptotically involves the trajectories of any initial point except fixed and periodic ones. We showed that the orbits are unstable and chaotic because Lyapunov exponent is non-negative.