@article{article_649122, title={On a Competitive System of Rational Difference Equations}, journal={Universal Journal of Mathematics and Applications}, volume={2}, pages={224–228}, year={2019}, DOI={10.32323/ujma.649122}, author={Gümüş, Mehmet}, keywords={System of difference equation,global asymptotic stability,equilibrium,rate of convergence}, abstract={<p style="text-align:justify;"> <span style="font-size:14px;"> </span> <span style="font-size:14px;">This paper aims to investigate the global stability and the rate of convergence of positive solutions that converge to the equilibrium point of the system of difference equations in the modeling competitive populations in the form $$ x_{n+1}^{(1)}=\frac{\alpha x_{n-2}^{(1) }{\beta +\gamma \prod\limits_{i=0}^{2}x_{n-i}^{(2) },\text{ }x_{n+1}^{(2)}=\frac{\alpha _{1}x_{n-2}^{(2) }{\beta _{1}+\gamma _{1}\prod\limits_{i=0}^{2}x_{n-i}^{(1)} }\text{, }n=0,1,... $$ where the parameters $\alpha ,\beta ,\gamma ,\alpha _{1},\beta _{1},\gamma _{1}$ are positive numbers and the initial conditions $ x_{-i}^{(1)},x_{-i}^{(2)}$ are arbitrary non-negative numbers for $i\in \{0,1,2\}$. </span> <br /> </p>}, number={4}, publisher={Emrah Evren KARA}