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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Dynamical Behavior of Some Recursive Exponential Difference Equations

Journal of Applied Nonlinear Dynamics 15(3) (2026) 533--548 | DOI:10.5890/JAND.2026.09.003

Abdul Khaliq$^{1}$, Muhammad Shabbir$^{2}$, Muhammad Zubair$^{1}$, Muhammad Rohail$^{1}$, Stephen Sadiq$^{3}$

$^{1}$ Department of Mathematics, Riphah International University, Lahore, Pakistan

$^{2}$ Department of Mathematics, University of Engineering and Technology, Lahore, Pakistan

$^{3}$ Department of Mathematics, Minhaj University, Lahore, Pakistan

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Abstract

In this paper, we study boundedness, persistence and rate of convergence of system of difference equations of exponential form \begin{equation*} r_{n+1}=\frac{\lambda +e^{-(\mu r_{n}+\xi s_{n})}}{\delta +\mu r_{n}+\xi s_{n}}, \ s_{n+1}=\frac{\lambda +e^{-(\mu s_{n}+\xi t_{n})}}{\delta +\mu s_{n}+\xi t_{n}}, \ t_{n+1}=\frac{\lambda +e^{-(\mu t_{n}+\xi r_{n})}}{\delta +\mu t_{n}+\xi r_{n}}, \end{equation*} where $n=0, 1, 2,\cdots$ and $\lambda $, $\mu $, $\xi $ and $\delta $ are non-negative constants and the initial conditions $r_{0}$, $s_{0}$, $t_{0}$ are non-negative real values.

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