MMN-5139
Dynamical behavior of a two dimensional difference equation system with quadratic term
Fei Jin; Qianhong Zhang; Ruiqi Yan;Abstract
This article deals with the equilibrium points, boundedness and persistence of the difference equation system $$ \mu_{n+1}=1+\hbar\frac{\mu_n}{\nu_{n-1}^2},\ \ \ \nu_{n+1}=1+\hbar\frac{\nu_n}{\mu_{n-1}^2},\ \ \ n\in\mathbb{N},$$ where the parameters $\hbar$ and the initial conditions $\mu_i,\nu_i$ $(i=-1,0)$ are all positive real numbers. We explored the global stability of discrete dynamic systems in the presence of a positive equilibrium point. In addition, an analysis of the convergence rate, which is crucial for such systems, is provided. Finally, numerical simulations are performed to confirm the effectiveness of the obtained results.
Vol. 27 (2026), No. 1, pp. 229-243