Boundedness of solutions and stability of certain second-order difference equation with quadratic term

Advances in Difference Equations

Emin Bešo¹  Esmir Pilav¹  Senada Kalabušić¹  Naida Mujić² 

[1] Department of Mathematics, University of Sarajevo;Faculty of Electrical Engineering, University of Sarajevo;

关键词: Difference equation;    Birkhoff normal form;    Boundedness;    Invariant set;    Neimark–Sacker bifurcation;    Stability;   

DOI  :  10.1186/s13662-019-2490-9

来源: DOAJ

【 摘 要 】

Abstract We 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.

【 授权许可】

Unknown