- Universal Journal of Mathematics and Applications
- Vol: 2 Issue: 4
- On a Competitive System of Rational Difference Equations
On a Competitive System of Rational Difference Equations
Authors : Mehmet Gümüş
Pages : 224-228
Doi:10.32323/ujma.649122
View : 8 | Download : 5
Publication Date : 2019-12-26
Article Type : Research
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 $$ x_{n+1}^{(1)}=\frac{\alpha x_{n-2}^{(1)}}{\beta +\gamma \prod\limits_{i=0}^{2}x_{n-i}^{(2)}},\text{ }x_{n+1}^{(2)}=\frac{\alpha _{1}x_{n-2}^{(2)}}{\beta _{1}+\gamma _{1}\prod\limits_{i=0}^{2}x_{n-i}^{(1)} }\text{, }n=0,1,... $$ 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 $i\in \{0,1,2\}$.Keywords : System of difference equation, global asymptotic stability, equilibrium, rate of convergence