Analytical Study of a System of Difference Equation
Abdualrazaq Sanbo, Elsayed M. Elsayed
Asian Research Journal of Mathematics · pp. 1–18 · Published 5 Jun 2019
10.9734/arjom/2019/v14i130118Abstract
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.
Cited by 3
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Ibraheem M. Alsulami, E. M. Elsayed · AIMS Mathematics · 2023
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