On the Global Asymptotic Stability and 4-Period Oscillation of the Third-Order Difference Equation

Abstract

The main objective of this paper is to study the global behavior and oscillation of the following third-order rational difference equation x n + 1 = α x n x n − 1 x n − 2 / β x n − 1 2 + γ x n − 2 2 , where the initial conditions x − 2 , x − 1 , x 0 are nonzero real numbers and α , β , γ are positive constants such that α ≤ β + γ . Visual examples supporting solutions are given at the end of the study. The figures are found with the help of MATLAB.