Existence and exponential convergence of almost periodic positive solution for Nicholson's blowflies discrete model with linear harvesting term

Abstract

This paper deals with a discrete Nicholson's blowflies model with linear harvesting term. By using contraction mapping fixed point theorem, we obtain sufficient conditions for the existence of unique almost periodic positive solution. Moreover, we investigate exponential convergence of the almost periodic positive solution by Lyapunov functional. Copyright © 2013 John Wiley & Sons, Ltd.

Existence and exponential stability of positive almost periodic solution for Nicholson’s blowflies models on time scales

“…Non of the results obtained in Chérif ( 2015 ), Duan and Huang ( 2015 ), Yao ( 2015a ), Wang et al. ( 2011 ), Alzabut ( 2010 ), Chen and Liu ( 2011 ), Long ( 2012 ), Wang ( 2013 ), Liu and Meng ( 2012 ), Xu ( 2014 ), Ding and Alzabut ( 2015 ), Yao ( 2014 ), Alzabut ( 2013 ) can be used to obtain the results of Example 3.…”

“…Hence, it is also important to study the dynamics of the discrete-time Nicholson’s blowflies model. Recently, authors of Yao ( 2014 ), Alzabut ( 2013 ) studied the existence and exponential convergence of almost periodic solutions for the discrete Nicholson’s blowflies model, respectively. In fact, it is troublesome to study the dynamics for continuous systems and their corresponding discrete ones respectively, therefore, it is significant to study that on time scales, which was initiated by Stefan Hilger (see Hilger 1990 ) in order to unify continuous and discrete cases.…”

Exponential extinction of discrete Nicholson's blowflies systems with patch structure and mortality terms

“…In comparison to the extensive investigation of these two equations in the literature, the study of the discrete Nicholson's model is considered to be seldom [10,20,24,25]. Indeed, the discrete counterpart of equation (1.2) has been lately attacked by the current authors in [2,3,23]. To the best of authors' observation, however, the discrete analogue of equation (1.3) has not been considered yet.…”