Global Behavior of Solutions to a Higher-Dimensional System of Difference Equations with Lucas Numbers Coefficients

Abstract

In this paper, we derive the well-defined solutions to a θ-dimensional system of difference equations. We show that, the well-defined solutions to that system are represented in terms of Fibonacci and Lucas sequences. Moreover, we study the global stability of the solutions to that system. Finally, we give some numerical examples which confirm our theoretical results.

Keywords

• Lucas numbers
• Fibonacci numbers
• system of difference equations
• global stability