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Computational Ecology and Software, 2020, 10(2): 44-58
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Article

Stability analysis of a system of second order rational difference equations

Muhammad Salman Khan1, Qamar Din2, Maria Habib1, Muhammad Asif Khan2
1Department of Mathematics, Quaid-I-Azam University Islamabad, 44230, Pakistan
2Department of Mathematics, University of the Poonch Rawalakot, Rawalakot 12350, Pakistan

Received 6 January 2020;Accepted 15 February 2020;Published 1 June 2020
IAEES

Abstract
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.

Keywords system of rational difference equations of order two;boundedness and persistence;existence of fixed point;linearized stability;global stability analysis;rate of convergence.



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