Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Stability and Boundedness Properties of a Rational Exponential Difference Equation

Version 1 : Received: 31 December 2019 / Approved: 31 December 2019 / Online: 31 December 2019 (17:13:44 CET)

How to cite: Leo Amalraj, J.; Manuel, M.S.; Kılıçman, A.; Dilip, D.S. Stability and Boundedness Properties of a Rational Exponential Difference Equation. Preprints 2019, 2019120420. https://doi.org/10.20944/preprints201912.0420.v1 Leo Amalraj, J.; Manuel, M.S.; Kılıçman, A.; Dilip, D.S. Stability and Boundedness Properties of a Rational Exponential Difference Equation. Preprints 2019, 2019120420. https://doi.org/10.20944/preprints201912.0420.v1

## Abstract

This article aims to discuss, the stability and boundedness character of the solutions of the rational equation of the form \begin{equation}\label{eql21.1} y_{t+1}=\frac{\nu\epsilon^{-y_t}+\delta\epsilon^{-y_{t-1}}}{\mu+\nu y_t+\delta y_{t-1}},\quad t\in N(0). \end{equation} Here, $\epsilon>1, \nu,\delta,\mu\in (0,\infty)$ and $y_0, y_1$ are taken as arbitrary non-negative reals and $N(a)=\{a,a+1,a+2,\cdots \}$. Relevant examples are provided to validate our results. The exactness is tested using MATLAB.

## Keywords

boundedness; equilibrium; global asymptotic stability; Rational Equation

## Subject

Computer Science and Mathematics, Applied Mathematics