On a Competitive System of Rational Difference Equations

Yıl 2019, , 224 - 228, 26.12.2019

Mehmet Gümüş

https://doi.org/10.32323/ujma.649122

Öz

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 $i\in \{0,1,2\}$.

Anahtar Kelimeler

System of difference equation, global asymptotic stability, equilibrium, rate of convergence

Kaynakça

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