A note on permanence for a nicholson's blowflies model with delay

Abstract

In this work, we will establish conditions to guarantee the permanence of the solution of the Nicholson's blowies model with delay (Formula Presented) where R; Γ : R -→ [0; ∞) are bounded continuous functions, r = sup t2R (t), Φ [-r; 0] -→ [0; ∞) is a continuous function with '(0) > 0, and δ; a : R -→ (0; ∞) are bounded continuous functions. More specifically, we will be interested in obtaining positive constants k and K such that, if x : [-r;∞) → R is the solution of the described system, then k ≤ lim t→1 inf x(t) ≤ lim t→1 sup x(t) ≤ K. Some numerical examples are provided to illustrate our results.