Analytical Study of a System of Difference Equation

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Abdualrazaq Sanbo
Elsayed M. Elsayed


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

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.

Dierence equations, Recursive sequences, Stability, Boundedness

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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.
Original Research Article