Abstract
In this paper, we are interested in a technique for solving some nonlinear rational systems of difference equations of third order, in three-dimensional case as a special case of the following system: x n + 1 = y n z n − 1 / y n ± x n − 2 , y n + 1 = z n x n − 1 / z n ± y n − 2 , and z n + 1 = x n y n − 1 / x n ± z n − 2 with initial conditions x − 2 , x − 1 , x 0 , y − 2 , y − 1 , y 0 , z − 2 , z − 1 , and z 0 are nonzero real numbers. Moreover, we study some behavior of the systems such as the boundedness of solutions for such systems. Finally, we present some numerical examples by giving some numerical values for the initial values 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.
Highlights
We believe that difference equations, referred to as recursive sequence, are a hot topic here as there has been increasing interest in the study of qualitative analysis of difference equations and systems of difference equations
A great effort has been made in studying the qualitative analysis of rational difference equations and rational difference system
Difference equations arise to study the national income of a country and its variation with time, Cobweb phenomenon in economics, etc
Summary
We believe that difference equations, referred to as recursive sequence, are a hot topic here as there has been increasing interest in the study of qualitative analysis of difference equations and systems of difference equations. In [37], Zhang et al studied the boundedness, the persistence, and global asymptotic stability of the positive solutions of the system of difference equations: xn yn− 1 xn− ryn−
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