Basins of Attraction of an Anti-competitive Discrete Rational System - Nurkanović, Mehmed; Nurkanović, Zehra (Sarajevo Journal of Mathematics, 2024)
We investigate the global asymptotic behavior of solutions of the following anti-competitive system of difference equations \begin{equation*} x_{n+1}=\frac{γ _{1}y_{n}}{A_{1}+x_{n}},\quad y_{n+1}=\frac{β _{2}x_{n}+γ _{2}y_{n}}{y_{n}},\quad n=0,1,…, \end{equation*} where the parameters $γ _1,γ _2,β _2,A_{1}$ are positive numbers and the initial conditions $x_{0}≥ 0,y_{0}>0$. We find the basins of attraction of all attractors of the system, which are the equilibrium point and period-two solutions. 2000 Mathematics Subject Classification. 37E30, 37G99, 39A10, 39A11