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

Afonso, S. M. [UNESP]; De Souza, C. S. [UNESP]

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

Data

2019-01-01

Autores

Afonso, S. M.

De Souza, C. S.

Tipo

Artigo

Resumo

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.