Asymptotics and Periodicity of Positive Solutions on a Nonlinear Rational System of Difference Equations

Abstract

The purpose of this paper is to discuss a nonlinear rational difference equation system with three variables. Firstly, by utilizing Jacobian theory, the stability of the system is obtained. Then, we explore the saddle point, nonhyperbolic point, and prime period-two solution and its boundedness. Finally, we verify the results obtained in the paper via computer numerical calculations.