Global dynamics of (1;2)-type systems of difference equations

Muhammad Naeem Qureshi; Abdul Qadeer Khan

doi:10.26637/MJM0602/0018

Abstract

We study the global dynamics of following $(1,2)$ - type systems of difference equations:
$$
\begin{aligned}
x_{n+1} & =\frac{\eta y_{n-1}}{1+\mu x_{n-2}^p}, y_{n+1}=\frac{\mu x_{n-1}}{1+\eta y_{n-2}^p}, \\
x_{n+1} & =\frac{\eta y_{n-1}}{1+\mu y_{n-2}^p}, y_{n+1}=\frac{\mu x_{n-1}}{1+\eta x_{n-2}^p},
\end{aligned}
$$
where $\eta, \mu, p$ and initial conditions $x_l, y_l, l=-2,-1,0$ are non-negative real numbers. Several numerical simulations are provided to support obtained results.

Keywords:

(1;2), equilibrium point, stability, rate of convergence

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

Muhammad Naeem Qureshi Department of Mathematics, University of Azad Jammu & Kashmir, Muzaffarabad 13100, Pakistan.
Abdul Qadeer Khan Department of Mathematics, University of Azad Jammu & Kashmir, Muzaffarabad 13100, Pakistan.

Pages: 408-416
Date Published: 01-04-2018
Vol. 6 No. 02 (2018): Malaya Journal of Matematik (MJM)

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