where a ∈[0,∞) and the initial values x-4 , x-3, x-2 , x-1, x0 ∈ (0,∞) . Mainly, the perturbation of the initial values may
lead to the essential variation of the cycle length rule for the nontrivial solutions of the equation. That is, with the change
of the initial values, the successive lengths of positive and negative semicycles for nontrivial solutions of this equation is
found to periodically occur with multiple different prime periods, respectively, 4 ,12 . Furthermore, in any one fixed
period, the successive occurring order of positive and negative semicycles is completely inverse, i.e., for the period 4 , the
order is either 3+ ,1- or 3- ,1+ in a period, and for the period 12 , the order is either 5+ ,2- ,1+ ,1- ,1+,2- or 5- ,2+ ,1+ ,1-,1+ ,2+ in a period. This rule is different from the known one we have obtained for various rational
difference equations. By the use of the rule its positive equilibrium point is verified to be globally asymptotically stable.