Dynamics Study and Solutions Expressions of Rational Discrete Systems

This article goal is to study the qualitative behaviors for the following rational difference systems U n +1 = d 1 U n −1 + a 1 V n −5 U n −1 / b 1 + e 1 V n −5 + V n −3 ( s 1 + c 1 V n −5 V n U n −4 U n −1 ), V n +1 = d 2 V n −1 + a 2 U n −5 V n −1 / b 2 + e 2 U n −5 + U n −3 ( s 2 + c 2 U n −5 U n V n −4 V n −1 ), namely, local asymptotic stable, global attractor of the equilibrium points and the boundedness of the positive solutions. Moreover, we will find the expressions of solutions for special case of the system. Additionally, we introduce numerical examples to illustrate the results.