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:
 
 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.
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