Abstract

In this paper, we get the form of the solutions of the following nonlinear recursive sequences of order four  where the initial conditionsare arbitrary real numbers. Also, we study some qualitative behaviors of the solutions as periodicity character of the solutions of these different equations and we obtain the equlibrium points of considered difference equations in order to investigate the local stability of these equlibrium points by using the linearized equation. We presented some numerical examples by giving some numerical values for the initial values and the coefficients of each case. Some figures have been given to explain the behavior of the obtained solutions in the case of numerical examples by using the mathematical program Matlab to confirm the obtained results.

Key words: Difference equations, recursive sequences, stability, periodic solution, Mathematics subject classification: 39A10.