  We consider a population with two equal dominated species, dynamics of which
is defined by one-dimensional piecewise-continuous, two parametric functions.
It is shown that for any non-zero parameters this function has two fixed points
and several periodic points. We prove that all periodic (in particular fixed)
points are repelling, and find 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. The limit sets analyzed by bifurcation diagrams. We give
biological interpretations of our results.
