Muhammad Salman Khan Qamar Din Maria Habib Muhammad Asif Khan Department of Mathematics, Quaid-I-Azam University Islamabad, 44230, Pakistan Department of Mathematics, University of the Poonch Rawalakot, Rawalakot 12350, Pakistan Computational Ecology and Software ISSN 2220-721X http://www.iaees.org/publications/journals/ces/online-version.asp 2020 10 2 44 58 International Academy of Ecology and Environmental Sciences Hong Kong 6 January 2020 15 February 2020 1 June 2020 system of rational difference equations of order two boundedness and persistence existence of fixed point linearized stability global stability analysis rate of convergence In this paper we consider a system of second order rational difference equations. We mainly discuss the boundedness and persistence, existence of fixed point, and uniqueness of positive fixed point, local and global behavior of positive fixed point and rate of convergence of every positive solution of the system under discussion. It will be shown that the system under discussion exhibits some special dynamics such as same mathematical condition for existence of fixed point and its global stability. Finally, some numerical examples are provided for verification of theoretical results. http://www.iaees.org/publications/journals/ces/articles/2020-10(2)/stability-analysis-of-a-rational-difference-equations.pdf