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

Advances in Difference Equations

article

Bešo, Emin¹  Kalabušić, Senada¹  Mujić, Naida²  Pilav, Esmir¹ 

[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

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

We consider the second-order rational difference equation $$ {x_{n+1}=\gamma +\delta \frac{x_{n}}{x^{2}_{n-1}}}, $$ where γ, δ are positive real numbers and the initial conditions $x_{-1}$ and $x_{0}$ 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】

CC BY