The third-order difference equation yn+1=a1yn21+yn2+a2yn−121+yn−12+a3yn−221+yn−22, as a potential discrete time model of population dynamics with three generation involved, is studied. The parts of the basins of attraction of three equilibrium points that this equation admits are described. Some results about period-two and period-three solutions have been established.
Kulenović et al. (Tue,) studied this question.