Analytical Study of a System of Difference Equation

Main Article Content

Abdualrazaq Sanbo
Elsayed M. Elsayed

Abstract

We study the qualitative behavior of a predator-prey model, where the carrying capacity of the predators environment is proportional to the number of prey. The considered system is given by the following rational difference equations:

$$x_{n+1}=\dfrac{x_{n} y_{n-2}}{y_{n-1} + y_{n-2}},\quad y_{n+1}=\dfrac{y_{n} x_{n-2}}{\pm x_{n-1} \pm x_{n-2}},\quad
n=0,1,\cdots,$$

where the initial conditions x-2; x-1; x0; y-2; y-1; y0 are arbitrary positive real numbers. Also, we give specic form of the solutions of some special cases of this equation. Some numerical examples are given to verify our theoretical results.

Keywords:
Dierence equations, Recursive sequences, Stability, Boundedness

Article Details

How to Cite
Sanbo, A., & Elsayed, E. M. (2019). Analytical Study of a System of Difference Equation. Asian Research Journal of Mathematics, 14(1), 1-18. https://doi.org/10.9734/arjom/2019/v14i130118
Section
Original Research Article