On a Competitive System of Rational Difference Equations

Authors : Mehmet GÜMÜŞ

Pages : 224-228

Doi:10.32323/ujma.649122

View : 14 | Download : 13

Publication Date : 2019-12-26

Article Type : Research Paper

Abstract : 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 $$ x_{n+1}^{insert ignore into journalissuearticles values(1);}=\frac{\alpha x_{n-2}^{insert ignore into journalissuearticles values(1);}}{\beta +\gamma \prod\limits_{i=0}^{2}x_{n-i}^{insert ignore into journalissuearticles values(2);}},\text{ }x_{n+1}^{insert ignore into journalissuearticles values(2);}=\frac{\alpha _{1}x_{n-2}^{insert ignore into journalissuearticles values(2);}}{\beta _{1}+\gamma _{1}\prod\limits_{i=0}^{2}x_{n-i}^{insert ignore into journalissuearticles values(1);} }\text{, }n=0,1,... $$ where the parameters $\alpha ,\beta ,\gamma ,\alpha _{1},\beta _{1},\gamma _{1}$ are positive numbers and the initial conditions $ x_{-i}^{insert ignore into journalissuearticles values(1);},x_{-i}^{insert ignore into journalissuearticles values(2);}$ are arbitrary non-negative numbers for $i\in \{0,1,2\}$.
Keywords : System of difference equation, global asymptotic stability, equilibrium, rate of convergence