Permanence and extinction of an impulsive delay competitive Lotka–Volterra model with periodic coefficients

In this paper, a periodic competitive system with delays and pulses is proposed. By using the comparison theorem for impulsive differential equations and the property of globally asymptotic stability of a periodic single-species growth population model with impulsive perturbations, sufficient conditions for permanence and extinction of the above system are derived, respectively. Our main results show that under appropriate conditions, the permanence and extinction of system are irrespective of the size of delays, however, impulsive perturbations play an important role and have effects on the permanence and extinction of system.