Application of Equilibrium Points in Solving Difference Equations and a New Class of Solvable Nonlinear Systems of Difference Equations

Abstract

There are so many classes of difference equations and systems which are solvable in closed form. So it is of some interest to find new methods and ideas which can be used in solving some of them. Here we show how equilibrium points can help in finding closed-form formulas for solutions to some difference equations and systems. We demonstrate the method for the case of a class of two-dimensional nonlinear systems of difference equations by showing their theoretical solvability. We also show that some of the systems are also practically solvable, by presenting closed-form formulas for their solutions or by explaining how the formulas can be obtained.