Global attractivity in delay “food-limited” models with exponential impulses ✩

In this paper, we are concerned with the global attractivity of the positive equilibrium of the following delay “food-limited” model with exponential impulses:  N (t )= p(t)N(t) 1−N(t−τ) 1+λN(t−τ), t 0, t = tk, N(t+k ) = N(tk )1+bk, k∈ N, where p ∈ PC([0,+∞)) with p >0, λ ∈ (0,+∞), τ >0, bk > −1 for all k ∈ N. The initial condition is x(t) = φ(t), t ∈ [−τ, 0], where φ ∈PC([−τ, 0]). The results obtained are new.  2003 Elsevier Inc. All rights reserved.