Exact Solutions and Stability of Fourth Order Systems of Difference Equations Using Padovan Numbers

Abstract

Difference equations are widely utilized to describe some phenomena arising in nonlinear sciences. In particular, systems of difference equations play an important role in investigating most nonlinear applications. Future behaviors of such phenomena can be sometimes known and understood by using exact solutions of systems of difference equations. Therefore, this article investigates the exact solutions of fourth order systems of difference equations. We use successive iterations and Padovan numbers to obtain the exact solutions in the form of rational functions. The stability of the considered systems are analyzed using Jacobian matrix. Real equilibrium points are found saddle. Under some selected parameters, we plot some 2D figures to show the behavior of the obtained solutions. The used methods can be successfully applied for high order systems of difference equations.