The authors consider several cyclic systems of difference equations of order 2 or 3 or higher order and analyse the global behaviour of their solutions. For instance, they study the system of difference equations of order 2 given by
where is a positive constant. By using the method of geometric unfolding of a difference equation, that is, by dealing with the associated discrete dynamical system, the authors obtain information about global periodicity (the case which was already considered in [B. Iričanin and S. Stević, Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 13, No. 3–4, 499–507 (2006; Zbl 1098.39003)] but using direct – and complicated – calculations) and other dynamical questions such as the localization of equilibrium points, and the global behaviour of the solutions lying in some invariant sets.
With the same strategy of the geometric unfolding, other systems considered in the paper are (here, is the cyclic permutation and ):
The systems of Lyness’ type difference equations of order two given by , where are appropriate rational maps (11 cases) of the real line;
the system given by , with , ;
the cycle system of Todd’s type difference equations of order three given by
the general cyclic system of equations of order given by