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9. 1. 2020.
Boundedness of solutions and stability of certain second-order difference equation with quadratic term
AbstractWe consider the second-order rational difference equation xn+1=γ+δxnxn−12,$$ {x_{n+1}=\gamma +\delta \frac{x_{n}}{x^{2}_{n-1}}}, $$ where γ, δ are positive real numbers and the initial conditions x−1$x_{-1}$ and x0$x_{0}$ are positive real numbers. Boundedness along with global attractivity and Neimark–Sacker bifurcation results are established. Furthermore, we give an asymptotic approximation of the invariant curve near the equilibrium point.