Solvability and Dynamical Analysis of Difference Equations

We obtain symmetries of a family of difference equations and we prove a relationship between these symmetries and similarity variables. We proceed with reduction and eventually derive formula solutions of the difference equations. Furthermore, we discuss the periodic nature of the solutions and analyze the stability of the fixed points. We use Lie point symmetry analysis as our tool in obtaining the solutions. Though we have analyzed a specific family of difference equations in this paper, the algorithmic techniques presented can be utilized to tackle many other difference equations.