Extinction and permanence of the numerical solution of a two-prey one-predator system with impulsive effect

The Euler method suitable to a two-prey one-predator system with impulsive effect on the predator of fixed moment is defined. The Euler method suitable to this system is defined. By using Floquet's theorem and small-amplitude perturbation skills, we show that a globally asymptotically stable two-pest eradication periodic solution exists when the impulsive period is less than some critical value. Further, we prove that the numerical system is permanence if the impulsive period is larger than some critical value, and meanwhile the conditions for the extinction of one of the two prey and permanence of the remaining two species are presented. Finally, some numerical experiments are given. Moreover, the discrete system is a special case if we take the stepsize h=1.