On the Bifurcation Behavior of Decoupled Systems of Difference Equations

This paper, we study systems of difference equations numerically and theoretically. These systems have been examined by many researchers. We focus on their general forms and limits. We consider different orders of difference systems. In certain cases, we use a computer in order to verify the summation laws that we encountered. We consider a system with two parameters. For certain values of the parameters, we determine the explicit form of the solution and show that the limit of this sequence tends to zero. We show that for the values of a parameter between 0 and 1, the limit of the sequence is a nonzero value, while for the values greater than 1, the limit of the sequence becomes zero.