The asymptotic dynamics of the classes of rational difference equations (RDEs) of third order defined over the positive real-line as

and

is investigated computationally with theoretical discussions and examples. It is noted that all the parameters a, b, c and the initial values  and  are all positive real numbers such that the denominator is always positive. Several periodic solutions with high periods of the RDEs as well as their inter-intra dynamical behaviours are studied.

rational difference equations, local asymptotic stability, periodic, quasi-periodic, fractal-like-trajectory.