Global stability problem of time-delayed Nicholson's Blowflies model for pseudo almost periodic solutions

Abstract

This brief investigates the existence and stability issue of the pseudo almost periodic solutions of time-delayed Nicholson's blowflies model (simply expressed as NB model). Firstly, we give an important result about the existence for the pseudo almost periodic solutions of the model via the pseudo almost periodic theories, the generalised Lyapunov methods and numerical algorithms. Secondly, we can ensure the asymptotic stability and global asymptotic stability of the pseudo almost periodic solutions of the considered model. Moreover, we deeply analyse the influence of initial desiring values and practical significance of the model. Finally, the benefits of the proposed control approach and the theoretical results are demonstrated by numerical example.